A residue theorem for polar analytic functions and Mellin analogues of Boas' differentiation formula and Valiron's sampling formula

Autor:	Bardaro, Carlo, Butzer, Paul L., Mantellini, Ilaria, Schmeisser, Gerhard
Rok vydání:	2019
Předmět:	Mathematics - Complex Variables Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	In this paper, we continue the study of the polar analytic functions, a notion introduced in \cite{BBMS1} and successfully applied in Mellin analysis. Here we obtain another version of the Cauchy integral formula and a residue theorem for polar Mellin derivatives, employing the new notion of logarithmic pole. The identity theorem for polar analytic functions is also derived. As applications we obtain an analogue of Boas' differentiation formula for polar Mellin derivatives, and an extension of the classical Bernstein inequality to polar Mellin derivatives. Finally we give an analogue of the well-know Valiron sampling theorem for polar analytic functions and some its consequences. Comment: 26 pages, 2 figures, and a dedication to Professor Domenico Candeloro
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.01854 Zobrazit plný text záznamu View this record from Arxiv