To the theory of generalized Stieltjes transforms

Autor:	Gomilko, Alexander, Tomilov, Yuri
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We identify measures arising in the representations of products of generalized Stieltjes transforms as generalized Stieltjes transforms, provide optimal estimates for the size of those measures, and address a similar issue for generalized Cauchy transforms. In the latter case, in two particular settings, we give criteria ensuring that the measures are positive. On this way, we also obtain new, applicable conditions for representability of functions as generalized Stieltjes transforms, thus providing a partial answer to a problem posed by Sokal and shedding a light at spectral multipliers emerged recently in probabilistic studies. As a byproduct of our approach, we improve several known results on Stieltjes and Hilbert transforms. Comment: 55 pages. This is a version of the paper to appear in Journal d'Analyse Mathematique
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.03474 Zobrazit plný text záznamu View this record from Arxiv