The Eighth Congress of Romanian Mathematicians

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List of talks

I. Algebra and Number Theory

Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu

II. Algebraic, Complex and Differential Geometry and Topology

Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties

III. Real and Complex Analysis, Potential Theory

IV. Ordinary and Partial Differential Equations, Variational Methods, Optimal Control

Special session: Optimization and Games Theory

V. Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics

Special session: Spectral Theory and Applications in Mathematical Physics

Special session: Dynamical Systems and Ergodic Theory

VI. Probability, Stochastic Analysis, and Mathematical Statistics

VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences

Special session: Mathematical Modeling of Some Medical and Biological Processes

Special session: Mathematical Models in Astronomy

VIII. Theoretical Computer Science, Operations Research and Mathematical Programming

Special session: Logic in Computer Science

IX. History and Philosophy of Mathematics

Real and Complex Analysis, Potential Theory 

(this list is in updating process)

University Of Crete, Greece
Title: Weak and strong type boundedness of Hardy-Littlewood maximal operator on weighted Lorentz spaces (details)
In this talk we will discuss the weak and strong type boundedness of Hardy-Littlewood maximal operator, $M$, on weighted Lorentz spaces. In fact, we will show that they are equivalent whenever $p>1$. The weighted Lorentz spaces generalize weighted Lebesgue spaces, as well as the classical Lorentz spaces, where the boundedness of $M$ is characterized by the $A_p$ and $B_p$ conditions, respectively. Thus, our characterization extends and unifies these results. Moreover, since the boundedness of $M$ is involved in the boundedness of the Hilbert transform, $H$, the aforementioned results over $M$ lead to a complete characterization of H on weighted Lorentz space. The results are based on joint works with J. Antezana, M. J. Carro, and J. Soria.
National Computer Science College "Spiru Haret", Suceava, Romania
Title: On Loewner domains in metric spaces (details)
This talk continues my results that were presented in [1], [2], [3] and [4]. The main purpose is to give some properties of a Loewner domain in a Q - Ahlfors regular space, Q>1. First, we shall prove that, in a locally path connected and Q - Ahlfors regular space, a bounded Q - Loewner domain is locally arc connected on the boundary and weakly quasiconformal accessible at each boundary point. Eventually, we deal with the extension theorems to boundary for quasiconformal mappings on domains in Q - Ahlfors regular spaces, when one of domain is a Q - Loewner domain. In [1], we have proved that if X and Y are complete Q - Ahlfors regular spaces, f:D→D′ is a metrically quasiconformal mapping, D⊂X and D′⊂Y are bounded Q - Loewner domains, then f can be extended to a homeomorphism f^{∗}:D→D′. We shall prove that, instead of complete spaces, we can assume proper spaces. In this case, f is a quasiconformal mapping in any sense. References [1] A. Andrei, Extension theorems for quasiconformal mappings in Ahlfors regular spaces, Math Reports 7(57), 3(2005), 167-178. [2] A. Andrei, Quasiconformal mappings in Ahlfors regular spaces, Rev. Roumaine Math. Pures Appl., 54(2009), 5-6, 361-373. [3] A. Andrei, Quasiconformal mappings on certain classes of domains in metric spaces, Buletin of the Univ. of Brasov, 5(54), 2012. [4] A. Andrei, On quasiextremal distance domains in metric spaces, Math. Reports 15(65), 4(2013), 319-329. [5] I. Heinonen, P. Koskela, Quasiconformal spaces with controlled geometry, Acta Math, 181 (1998), 1-61. [6] O. Martio, V. Ryazanov, U. Srebro and E. Yakubov, Moduli in the modern mapping theory, Springer, New York, 2009.
"Al. I. Cuza" University of Iasi, ROMANIA
Title: Semiliniarity of space of sn-bounded multifunctions (details)
In this talk we study a metric stucture on the space of sn-bounded set-valued functions. Thus we introduce a metric d₁ of supremum type and a near metric d₂ defined by a Sugeno integral, and compare the induced topologies τ₁ and τ₂. We also study the translated topology τ₃ of τ₁ and establish sufficient and characteristic conditions for τ₃ to be semi-linear.
University of Borås, Sweden
Title: A Cauchy Functional Inequality (details)
In this presentation we give a solution to a moment problem related to the Cauchy Functional Equation on commutative semigroups. A result related to potential theory is also obtained.
Mersin University, Department of Mathematics, Turkey
Title: Approximation by generalized deferred Ces\'{a}ro means in the space $H_{p}^{\omega}$ (details)
The deferred Ces\'{a}ro transformations which have useful properties not possessed by the Ces\'{a}ro transformation was considered by R.P. Agnew in \cite{Agn}. In \cite{DK}, De\v{g}er and K\"{u}\c{c}\"{u}kaslan introduced a generalization of deferred Ces\'{a}ro transformations by taking account of some well known transformations such as Woronoi-N\"{o}rlund and Riesz, and considered the degree of approximation by the generalized deferred Ces\'{a}ro means in the space $H(\alpha,p)$, $p\geq1$, $0<\alpha\leq1$ by concerning with some sequence classes. In 2014, Nayak \emph{et al.} studied the rate of convergence problem of Fourier series by Deferred Ces\'{a}ro Mean in the space $H_{p}^{\omega}$ introduced by Das \emph{et al.} in \cite{DNR}. In this studying, we shall give the degree of approximation by the generalized deferred Ces\'{a}ro means in the space $H_{p}^{\omega}$. Therefore the results given in \cite{NDR} are generalized according to the summability method. \bibitem{Agn} R. P. Agnew, On deferred Ces\'{a}ro means. Ann. Math. (2) 33(3), (1932), 413--421. \bibitem{DNR} G. Das, A. Nath and B. K. Ray, An estimate of the rate of convergence of Fourier series in generalized H\"{o}lder metric, Analysis and Applications (Ujjain,1999), Narosa (New Delhi, 2002 ), 43--60. \bibitem{DK} U. De\u{g}er and M. K\"{u}\c{c}\"{u}kaslan, "A generalization of deferred Cesaro means and some of their applications", Journal of Inequalities and Applications, 2015(1), (2015), 1--16. \bibitem{NDR} L. Nayak, G. Das and B. K. Ray, An estimate of the rate of convergence of Fourier series in the generalized H\"{o}lder metric by Deferred Ces\'{a}ro Mean, Journal of Mathematical Analysis and Applications, 420(1), (2014), 563--575.
Université d'Oran 1, ALGERIA
Abstract We give minimal conditions on the space X, such that a good part of potential theory in the frame of excessive structure, associated with a proper submarkovian resolvent family of kernels on X, may be developed. We characterize the regular excessive elements as being those excessive functions for which the pseudobalayages associated with, are balayages and we construct a fine carrier theory without use any kind of compactification.
University of Prishtina, Kosovo
Title: On some $l_p$-type inequalities involving quasi monotone and quasi lacunary sequences (details)
We give some $l_p$-type inequalities about sequences satisfying certain quasi monotone and quasi lacunary type properties. As special cases, reverse $l_p$-type inequalities for non-negative decreasing sequences are obtained. The inequalities are closely related to Copson's and Leindler's inequalities, but the sign of the inequalities is reversed. We also give an application of the inequalities in Foruier analysis.
BRACCI Filippo
Università di Roma "Tor Vergata", Italia
Title: Univalent mappings, Horosphere boundary and prime end theory in higher dimension (details)
We give an account of the theory of univalent mappings in the ball of higher dimension, highlighting the difference between the one dimensional case and the higher dimensional one (density of automorphisms, existence of bounded support functions in the class S^0). We also describe an new approach on complete hyperbolic complex manifolds in order to define an abstract boundary by means of suitable sequences which can be seen as "horosphere sequences", and that can be considered a prime end type theory in higher dimension. All biholomorpisms extend to homeomorphisms on such horosphere boundaries. As a consequence we give some applications of this construction to study the boundary behavior of univalent mappings in the unit ball.
BREAZ Daniel
"1 Decembrie 1918" University of Alba Iulia, Romania
Title: Some new classes of analytic functions (details)
In this talk I present some new classes of analytic functions. Some sufficient conditions are proved and some connections with other known classes are presented.
BREAZ Nicoleta
"1 Decembrie 1918" University of Alba Iulia, Romania
Title: Mocanu and Serb univalence criteria for some integral operators (details)
We obtain Mocanu and Serb type univalence criteria for two general integral operators defined by analytic functions in the open unit disk.
BUCUR Gheorghe
Institutul de Matematica "Simion Stoilow", Romania
Title: Generalized Arzela-Ascoli theorem and applications (details)
For any two arbitrary sets $X$ and $Y$ and any function $f$ defined on the cartesian product $X \times Y$ with values in a metric space, we state a very general Arzela-Ascoli result. The function $f$ has some compact property with respect to $X$ if and only if it has this property with respect to $Y$. We give several applications of this general result.
BUCUR Ileana
Universitatea de Tehnica de Constructii Bucuresti, Romania
Title: Fixed point theory and contractive sequences (details)
In an abitrary metric space $X$ we introduce the notion of contractive sequence and we show that if $X$ is complete then such sequences are convergent. Some applications to the fixed point theory are given.
CAZACU Cristian
University ``Politehnica" of Bucharest & ``Simion Stoilow" Institute of Mathematics of the Romanian Academy, Romania
Title: Optimal Hardy constants for Schrodinger operators with multi-singular inverse-square potentials (details)
In this talk we consider the optimization problem $\mu^\star(\Omega):=\inf \left(\int_\Omega |\nabla  u|^2  dx\big/ \int_\Omega V u^2 dx\right)$, where $V$ is a multi-singular potential with $n$ singular poles ($n\geq 2$) which arise either in the interior or on the boundary of a  smooth bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq 2$. First we prove that whenever $\Omega$ contains all the singularities in the interior, then $\mu^\star(\Omega)>\mu^\star(\mathbb{R}^N)$ if $n\geq 3$ and $\mu^\star(\Omega)=\mu^\star(\mathbb{R}^N)$ when $n=2$ (It is known that $\mu^\star(\mathbb{R}^N)=(N-2)^2/n^2)$. Furthermore, we also analyze the situation in which all the poles are located on the boundary. In this case, we obtain a new critical barrier for the best Hardy constant corresponding to $V$, which is $\mu^\star(\Omega)=N^2/n^2$. In addition, we also discuss the attainability of $\mu^\star(\Omega)$. A special case for the non-attainability of $\mu^\star(\Omega)$ corresponds to the bipolar case $n=2$.
The University of Sydney, Australia
Title: Existence and classification of singular solutions to nonlinear elliptic equations with a gradient term (details)
In this talk, we present a complete classification of the behaviour near $0$ (and at $infty$ when $Omega=mathbb R^N$) of all positive solutions of $Delta u = u^q |nabla u|^m$ in $Omega setminus { 0 }$, where $Omega$ is a domain in $mathbb{R}^N$ ($N geq 2$) and $0in Omega$. Here, $qgeq 0$ and $min (0,2)$ satisfy $m+q>1$. Our classification depends on the position of $q$ relative to the critical exponent $q_*:=frac{N-m,(N-1)}{N-2}$ (with $q_*=infty$ if $N= 2$). We prove the following: If $q< q_*$, then any positive solution $u$ has either (1) a removable singularity at $0$, or (2) a {em weak singularity} at $0$, or (3) $lim_{|x|to 0} |x|^{vartheta} u(x)=lambda$, where $vartheta$ and $lambda$ are uniquely determined positive constants (strong singularity). If $qgeq q_*$ (for $N>2$), then $0$ is a removable singularity for all positive solutions. Furthermore, any positive solution in $mathbb{R}^Nsetminus{0}$ is either constant or has a weak/strong singularity at $0$. The latter is possible only for $q1$ when all solutions decay to $0$. We also provide sharp existence results, emphasising the more difficult case of $min (0,1)$ where new phenomena arise. This is joint work with Joshua Ching (The University of Sydney).
University of Bucharest, Faculty of Mathematics and Computer Sciences, Romania
Title: Some properties of open discrete ring mappings (details)
We study the properties of open, discrete ring mappings satisfying generalized modular inequalities, namely the equicontinuity, the distortion and the limit mapping of certain homeomorphisms from these classes. Such mappings generalize the known class of quasiregular mappings and their extensions known as mappings of finite distortion. We apply our results to open discrete ring mappings f : D included in Rn → Df included in Rn satisfying condition (N) and having local ACLq inverses, and we focus especially on the case n 􀀀 1 < q < n. We show that such mappings cannot have essential singularities and also that Zoric's theorem can hold in this case and in some conditions even if n = 2. This is in contrast even with the known case of quasiregular mappings.
Mersin Universit, Department of Mathematics, Turkey
Title: On Approximation by Matrix Means of the Multiple Fourier Series in the H\ (details)
Suppose that $f(x,y)$ is integrable in the sense of Lebesgue over the square $S^2:= S(-\pi,\pi;-\pi,\pi)$ and of period $2\pi$ in $x$ and in $y$. In \cite{Step 1973} and \cite{Step 1974}, A. I. Stepanets has been investigated the problem of the approximation of functions $f(x,y)$ by the partial sums of their Fourier sums under the some conditions. S. Lal has been studied the approximation of functions belonging to Lipschitz class by matrix summability method for double Fourier series under the uniform norm in \cite{Lal}. Naturally, there has arisen the problem of considering similar questions also in the case of periodic functions of two variables in the H\"{o}lder metric. In this work, we shall give the degree of approximation to functions belonging to H\"{o}lder class by matrix summability method of multiple Fourier series in the H\"{o}lder metric. \bibitem{Step 1973} A. I. Stepanets, The approximation of certain classes of diferentiable periodic functions of two variables by Fourier sums, Ukrainian Mathematical Journal(Translated from Ukrainskii Matematieheskii Zhurnal, Vol. 25, No. 5, pp. 599-609, September-October, 1973), 26, (1973) 498–-506. \bibitem{Step 1974} A. I. Stepanets, Approximation of certain classes of periodic functions of two variables by linear methods of summation of their Fourier series, Ukrainian Mathematical Journal(Translated from Ukrainskii Matematieheskii Zhurnal, Vol. 26, No. 2, pp. 205-215, March-April, 1974), 26, (1974) 168–-179. \bibitem{Lal} S. Lal, On the approximation of function $f(x,y)$ belonging to Lipschitz class by matrix summability method of double Fourier series, Journal of the Indian Math. Soc. (78)1-4, (2011), 93–-101.
Indiana University, Bloomington, USA
Title: Decouplings and applications to Number Theory and PDEs (details)
We discuss a new Fourier analytic approach to estimating a wide variety of exponential sums. Applications include estimates for the number of solutions to various Diophantine inequalities, Vinogradov mean value-type theorems and progress on the Lindelof hypothesis. Among the consequences in PDEs, we will mention the sharp Strichartz estimates on the higher dimensional torus and progress on the local smoothing equation.
Faculty of Mathematics, "Al. I. Cuza" University, Iasi, Romania
Title: Direct methods through convergence in measure (details)
\documentclass{article} \begin{document} Tonelli's direct method provides conditions on $H$ and $f$ that ensure the existence of a solution for the problem $$\inf_{u\in H}\int_{\Omega}f(t,u(t),\nabla u(t)) dt,\leqno(P)$$where, generally, $H$ is equipped with a weak topology. In this contribution we study the continuity of integral and the compactness of minimizing sequences for the above problem with respect to the topology of convergence in measure on $H$. \end{document}
York University, Canada
Title: On the Location of the Zeros of Bohr Functions (details)
Given a general Dirichlet series, a basis is attached to the sequence of exponents. With the corresponding Bohr matrix, a Bohr function is defined. We are studying the location of the zeros of such a function.
Babes-Bolyai University, Cluj-Napoca, Romania
Title: Compactness and density of certain reachable families of the Loewner ODE in $\mathbb{C}^n$ (details)
In this talk we focus on the control-theoretic approach to the Loewner ODE, developed by O. Roth in $\mathbb{C}$ and by I. Graham, H. Hamada, G. Kohr, M. Kohr in $\mathbb{C}^n$. We present some results concerning compactness and density of certain normalized time-$T$-reachable families of the Loewner ODE in $\mathbb{C}^n$, where $T\in[0,infty]$. Then we study some generalizations suggested by the last mentioned authors. In particular, we prove a generalization to $\mathbb{C}^n$ of a well-known result due to Loewner from 1923.
IONITA George - Ionut
University Politehnica of Bucharest and "Simion Stoilow" Institute of Mathematics of the Romanian Academy, Romania
Title: q-completeness and q-completeness with corners of unbranched Riemann domains (details)
documentclass[a4paper,12pt]{article} usepackage{amsmath, amsthm, amssymb} begin{document} %-------------- begin{abstract} In 2007 Colc toiu and Diederich showed that if $p:Yrightarrow X$ is a Riemann domain between complex spaces with isolated singularities such that $X$ is Stein and $p$ is a Stein morphism, then $Y$ is Stein. In the following we will improve the above mentioned result in two ways: begin{itemize} item[-] we suppose that $X$ is $q$-complete and we obtain that $Y$ is $q$-complete; item[-] we suppose that the morphism $p$ is locally $q$-complete with corners and we obtain that $Y$ is $q$-complete with corners. end{itemize} end{abstract} end{document}
Institut de Mathematiques de Jussieu, Univ. Pierre et Marie Curie, Franta
Title: Non existence of Levi flat hypersurfaces with positive normal bundle in compact K (details)
In 1993 D. Cerveau conjectured the non existence of smooth Levi flat real hypersurfaces in the complex $n$-dimensional projective space ${mathbb CP}_n$, $n geq 2$. The conjecture was proved for $ngeq 3$ by A. Lins Neto in 1999 for real analytic Levi flat hypersurfaces and by Y.-T. Siu in 2000 for $C^{12}$ smooth Levi flat hypersurfaces. It is still open for $n = 2$. A principal element in the proof of the non existence of smooth Levi flat hypersurfaces in ${mathbb CP}_n$ for $ngeq 3$ is that the Fubini-Study metric induces a metric with positive curvature on every quotient of the tangent space. In 2008, M. Brunella proved that the normal bundle to the Levi foliation of a closed real analytic Levi flat hypersurface in a compact K"ahler manifold of dimension $ngeq 3$ does not admit any Hermitian metric with leafwise positive curvature. He conjectured that this is also true for $C^infty$ Levi flat hypersurfaces. In this talk, we will give a proof to this conjecture of M. Brunella.
IMAR, Romania
Title: Finite coverings of complex spaces by connected Stein open sets (details)
We prove that every connected complex space has a finite covering by connected Stein open subsets.
KOHR Gabriela
Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania
Title: The generalized Loewner differential equation in higher dimensions. Applications to extremal problems for biholomorphic mappings (details)
In this talk we survey classical and also recent results related to the generalized Loewner differential equation on the Euclidean unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$. We also present applications in the study of extreme points and support points for the family $S_A^0(\mathbb{B}^n)$ of mappings with $A$-parametric representation, i.e. normalized biholomorphic mappings $f$ on $\mathbb{B}^n$ which can be imbedded in normal Loewner chains $f(z,t)=e^{tA}z+\cdots$ such that $f=f(\cdot,0)$, where $A\in L(\mathbb{C}^n)$ with $k_+(A)<2m(A)$. Here $k_+(A)$ is the Lyapunov index of $A$ and $m(A)=\min\{\Re\langle A(z),z\rangle:\|z\|=1\}$. We also use some control theoretical methods to discuss the case of reachable families of biholomorphic mappings generated by the generalized Loewner differential equation on $\mathbb{B}^n$. Certain open problems and conjectures are also considered. Finally, we point recent related results due to F. Bracci, O. Roth, and S. Schleissinger. Joint work with Ian Graham (Toronto), Hidetaka Hamada (Fukuoka), and Mirela Kohr (Cluj-Napoca)
LIE Victor
Purdue University, United States
Title: Extremizers for the 2D Kakeya problem (details)
$\newline$ \underline{\textbf{Abstract}}: Our talk will adress the following theme $\newline$ \noindent\textsf{Formulation of the problem.} Let $Q_0$ be the unit square and let $\mathbf{T}$ be a collection of $M^{2n}$ separated tubes inside $Q$ having length one and width $M^{-2n}$ for some large $M,\,n\in\mathbb{N}$. Assume that $\mathbf{T}=\mathbf{T}_1\cup\mathbf{T}_2$ with $\mathbf{T}_1$ consisting of tubes that have slopes between $[-1,-\frac{9}{10}]$ and $\mathbf{T}_2$ having tubes with slopes in $[\frac{9}{10},\,1]$ . Our goal is to understand \textit{both the structure and the size} of the level sets $$\{F>\alpha\}$$ where $\alpha>0$ and $F:=(\sum_{\tau\in\mathbf{T}_1}\chi_{\tau})(\sum_{\tau\in\mathbf{T}_2}\chi_{\tau})$ stands for the bilinear Kakeya function. Our analysis will involve additive combinatorics (e.g. Plunnecke sum-set estimate) and incidence geometry (e.g. Szemeredi-Trotter inequality) techniques and relates with a class of problems including Bourgain's sum-product theorem and Katz-Tao ring conjecture. This is a joint work with Michael Bateman.
MARCOCI Anca Nicoleta
Technical University of Civil Engineering Bucharest, Romania
Title: Improved Sobolev inequalities in the classical Lorentz spaces (details)
In this talk we present refined Sobolev inequalities using as base space classical Lorentz spaces associated to a weight from the Arino-Muckenhoupt class. This class of weights appeared in a paper of M. A. Arino and B. Muckenhoupt from 1990, in connection with the Hardy inequality with weights for non-increasing functions. This talk is based on a joint work with D. Chamorro and L. Marcoci.
MARCOCI Liviu Gabriel
Technical University of Civil Engineering Bucharest, Romania
Title: On some factorization results (details)
G. Bennett in 1996 studied some classical inequalities from the point of view of factorization between some spaces of sequences. In this talk we present some factorizations in the case of weighted function spaces. In particular, we derive the best constants in some weighted inequalities.
Transilvania University of Brasov, Romania
Title: An improvement of Gruss inequality (details)
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Lumina - University of South-East Europe, Bucharest, Romania
Title: On some properties of Tsallis hypoentropies and hypodivergences (details)
The aim of this presentation is to extend Ferreri's hypoentropy to the Tsallis statistics. We introduce the Tsallis hypoentropy and the Tsallis hypodivergence and describe their mathematical behavior. Fundamental properties like nonnegativity, the chain rule and subadditivity are established.
MOCANU Marcelina
"Vasile Alecsandri" University of Bacău, Romania
Title: Cheeger differentiable Orlicz-Sobolev functions on metric spaces (details)
We prove sufficient conditions for the Cheeger differentiability a.e. of the functions in the Orlicz-Sobolev space $N^{1,\Phi }\left( X\right) $, where $% \left( X,d,\mu \right) $ is a doubling metric measure space and $\Phi $ is a Young function. We also study the $L^{\Phi _{s}}-$differentiability of the functions in $N^{1,\Phi }\left( X\right) $, where $\Phi $ satisfies some Calder\'{o}n-type growth conditions. Here $\Phi _{s}$ denotes the Sobolev conjugate of $\Phi $ with respect to the homogeneous dimension $s$ of $X$. In the special case where $\Phi \left( t\right) =t^{p}$ \ with $1\leq p<\infty $ and $p>s-1$ we prove that every monotone function in $% N_{loc}^{1,\Phi }\left( X\right) $ (in particular, every continuous quasiminimizer for the $p-$Dirichlet energy integral) is Cheeger differentiable a.e. Our main tool is the extension of Stepanov's differentiability theorem to metric measure spaces, proved by Balogh, Rogovin and Z\"{u}rcher.
Cornell University, USA
Title: Iterated Fourier series (details)
The goal of the lecture is to describe a natural bridge which connects the KdV equation to the absolute Galois group. The "pillars" of this bridge turned out to be the analytical objects from the title.
NEAGU Vasile
Moldova State University, Republic of Moldova
As it is known, the Noether theorems play an important role in the theory of singular integral equations. A singular integral operator with a Carleman shift is defined to be the operator of the formrnbegin{equation} label{GrindEQ__1_}rnleft(Mvarphi right)left(tright)=sum^n_{k=0}{left{a_kleft(tright)varphi left({alpha }_kleft(tright)right)+frac{b_k(t)}{pi i}int_{Gamma }{frac{varphi (tau )}{tau -{alpha }_kleft(tright)}}dtau right}}, rnend{equation}rnwhere $a_k , b_k$ are function given on the contour ${rm Gamma }$.rnrnnoindent In the present paper on the least subalgebra $sum $of the algebra$ L(L_p({rm Gamma },rho ))$, containing all operators of the form eqref{GrindEQ__1_} with piecewise continuous coefficients, is studied. It is necessary to consider separately the case, when$ alpha $ preserves the orientation on ${rm Gamma }$$,$ and the case, when$ alpha $ reverses' the orientation. The algebra $sum $contains the set $sum _{0} $ of all sums of compositions of operators of the form eqref{GrindEQ__1_}, and also operators, which are limits (in the sense of convergence by the norm of operators) of a sequence of operators from$sum _{0} . $ The research of the set $sum _{0} $is based on the suggested by I.Gohberg and N.Krupnik method of the study of „textit{complicated}'' operators, which allows to receive necessary and sufficient conditions of Noetherian property of operators from $sum . $ In the paper the existence of such an isomorphism between $sum $and some algebra textit{A} of singular integral operators with a Cauchy kernel that an arbitrary operator from $sum $and its image are simultaneously Noetherian or not Noetherian is proved. It allows to intoduce the concept of a symbol for all operators from $sum $and, using known results for algebra textit{A}, in terms of a symbol to receive conditions of Noetherian property for all operators from $sum , $ including for $sum backslash sum _{0} .$ Through the symbol the index of operators$Ain sum $can be also expressed.rnrnnoindent The set of values of the determinant of a symbol $A(t,xi )$ represents a closed continuous curve, which can be oriented in natural way. The index of this curve (i.e. the number of turns about the origin), taken with the opposite sign, is equal to the index of the operator $A.$
NISHIO Masaharu
Osaka City University, Japan
Title: Harmonic Bergman spaces with radial measure weight on the ball (details)
We consider harmonic Bergman spaces on the ball. In this talk, we deal with space with radial measure weight. For two radial measures, we introduce an averaging function, to give the conditions for corresponding Toeplitz operators to be bounded and compact. We also discuss the boundary behavior of the harmonic Bergman kernels.
OPRINA Andrei - George
Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania
Title: Perturbations with kernels of the generator of a Markov process (details)
We present the perturbation with kernels of the generator of a Markov process. Our approach avoids any transience hypothesis and it is motivated by recent applications in infinite dimensional situations: measure-valued branching processes and the associated nonlinear equations, quasi-regular generalized Dirichlet forms. The talk is based on joint works with Lucian Beznea.
OROS Georgia Irina
University of Oradea, Faculty of Sciences, Romania
The concept of strong di fferential subordination was introduced in by J.A. Antonino and S. Romaguera using the classical notion of differential subordination introduced by S.S.Miller and P.T.Mocanu. This concept was developed by the authors of the present paper in a series of papers. The concept of strong diff erential superordination was introduced by G.I.Oros, like a dual concept of the strong di fferential subordination and developed by the authors in other papers. In this paper, we study certain strong di fferential superordinations, obtained by using a new integral operator previously introduced in the paper G.I. Oros, Gh. Oros, R. Diaconu, Di fferential subordinations obtained with some new integral operators, J. Computational Analysis and Application, 19(2015),no. 5, 904-910.
PASCU Nicolae
Kennesaw State University, USA
Title: Univalence Criteria for analytic functions defined in non-convex domains (details)
We consider two general classes of non-convex domains: the first class consists of simply connected planar domains characterized by a certain deformation from convexity given by the convexity constant of the domain, the second being the class of ϕ-convex domains introduced by M. O. Reade. We derive new univalence criteria for analytic functions defined on these classes of non-convex domains which generalize some well known univalence criteria (Ozaki - Nunokawa univalence criterion).
PREDA Ovidiu
"Simion Stoilow" Institute of Mathematics of the Romanian Academy, Romania
Title: Locally Stein Open Subsets in Normal Stein Spaces (details)
We present a result related to the local Steinness problem: if $Omega$ is a locally Stein open subset of a Stein space $X$, does it follow that $Omega$ is itself Stein? We will prove that if $X$ is normal, then for every sequence of points $(x_n)_n$ which tends to a limit $xin partial Omega setminus Sing(X)$, there exists a holomorphic function $f$ on $Omega$ which is unbounded on $(x_n)_n$. Then, we will use this result to obtain a characterisation theorem for a particular case of the Serre problem.
SALAGEAN Grigore Stefan
Babes-Bolyai University Cluj-Napoca, Romania
Title: Some characteristic properties of analytic functions (details)
We consider a class of analytic functions defined in the open unit disk satisfying a certain subordination condition where is used a differential operator We obtain some characteristic properties giving the coefficient inequality, radius and subordination results, and an inclusion result for the above class. Sharp bounds for the initial coefficient and for the Fekete-Szegö functional are determined, and also some integral representations are given.
SYMEONIDIS Eleutherius
Katholische Universitaet Eichstaett-Ingolstadt, Germany
Title: Harmonic families of closed surfaces (details)
The mean value property of harmonic functions and other quadrature identities result by passing to the limit in families of surfaces, over which every harmonic function has the same mean value.
VLADOIU Speranta
University of Bucharest, Romania
Title: Markov Processes on the Lipschitz Boundary for the Neumann and Robin Problems (details)
We investigate the Markov process on the boundary of a bounded Lipschitz domain associated to the Neumann and Robin boundary value problems. We first construct $L^p$-semigroups of sub-Markovian contractions on the boundary, generated by the boundary conditions and we show that they are induced by the transition function of the forthcoming processes. As in the smooth boundary case the process on the boundary is obtained by the time change with the inverse of a continuous additive functional of the reflected Brownian motion.
Mersin University, Department of Mathematics, Turkey
Title: On Some Spaces of Sequences of Interval Numbers (details)
Interval arithmetic was first suggested by Dwyer in \cite{Dwyer1}. In \cite{Chiao1}, Chiao introduced the sequences of interval numbers and defined usual convergence of sequences of interval number. Esi and Yasemin G\"{o}lbol in \cite{Esi6} defined the metric spaces $\overline{c}_{0}(f,p,s)$, $\overline{c}(f,p,s)$, $\overline{l}_{\infty}(f,p,s)$ and $\overline{l}_{p}(f,p,s)$ of sequences of interval numbers by a modulus function. In this study, we consider a generalization of these metric spaces. For this aim, let $\psi(k)$ be a positive function for all $k\in N$ such that \begin{equation}\label{1}\lim_{k\rightarrow\infty}\psi(k)=0,\end{equation} \begin{equation}\label{2}\Delta_{2}\psi(k)=\psi(k-1)-2\psi(k)+\psi(k+1)\geq0.\end{equation} Therefore, according to class of functions which satisfying the conditions (\ref{1}) and (\ref{2}) we deal with the metric spaces $\overline{c}_{0}(f,p,\psi)$, $ \overline{c}(f,p,\psi)$, $ \overline{l}_{\infty}(f,p,\psi)$ and $\overline{l}_{p}(f,p,\psi)$ of sequences of interval numbers defined by a modulus function and state some topological and inclusion theorems related to these spaces. \bibitem{Esi6} A. Esi and S. Yasemin G\"{o}lbol, Some spaces of sequences of interval numbers defined by a modulus function, Global Journal of Mathematical Analysis, \textbf{2}, (1)(2014), 11--16. \bibitem{Chiao1} K. P. Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematics. \textbf{18}, (2)(2002), 219--233. \bibitem{Dwyer1} P. S. Dwyer, Linear Computation, Wiley, New York, 1951.