Vă invităm sa participați la următoarele conferințe susținute de Prof. Toshiyuki Sugawa (Tohoku University, Sendai) și Prof. Anatoly Golberg (Holon Institute of Technology) , în cadrul seminarului de Analiză Complexă, în data de 23.06.2025 (luni), ora 10:00, sala pi, cladirea Mathematica.

Toshiyuki Sugawa: Totally monotone sequences and hypergeometric functions

Abstract

We consider the problem to ask when the hypergeometric function F(a,b;c;z) is the generating function of a totally monotone sequence in terms of the complex parameters a,b and c. This is contained in the classical work of Gauss when b=1. We present a necessary and sufficient conditions for that. As a consequence, we also give a necessary and sufficient condition for the shifted hypergeometric function zF(a,b;c;z) is universally starlike. The sufficiency was proved by Küstner in 2002. We can indeed show that it is also necessary. The talk is based on joint work with Li-Mei Wang.

Anatoly Golberg: Weakly Lipshchitz mappings in higher dimensions„.

Abstract.
In one dimension, Lipschitz continuity serves as a natural bridge between continuous differentiability and absolute continuity. However, this relatively simple picture becomes significantly more intricate in higher dimensions. Despite this added complexity, Lipschitz mappings retain a wealth of important properties and find numerous applications. Classical results, such as the McShane and Kirszbraun extension theorems, alongside the preservation of Hausdorff dimension, underscore the significance of these mappings. This talk delves into the fascinating and multifaceted theory of Lipschitz functions in the higher-dimensional setting.

We will introduce a weakly Lipschitz condition defined by $\limsup_{y\to x}|f(x)-f(y)|/|x-y|\le \Phi'(x)^{1/n},$ where $\Phi'(x)$ represents the derivative of a set function $\Phi.$ Under this assumption, we establish that the mapping $f$ is absolutely continuous on almost all lines parallel to the coordinate axes (an ACL-mapping) and belongs to the Sobolev class $W^{1,n}_{\rm loc}.$ Furthermore, we demonstrate that any metrically quasiconformal mapping is weakly Lipschitz in this defined sense.