Integration of polar-analytic functions and applications to Boas’ differentiation formula and Bernstein’s inequality in Mellin setting-Reference-Cited by-同舟云学术

Integration of polar-analytic functions and applications to Boas’ differentiation formula and Bernstein’s inequality in Mellin setting

Published:2020-05-28 Issue:4 Volume:13 Page:503-514
ISSN:1972-6724
Container-title:Bollettino dell'Unione Matematica Italiana
language:en
Short-container-title:Boll Unione Mat Ital

Author:

Bardaro Carlo,Butzer Paul L.,Mantellini Ilaria,Schmeisser Gerhard^ORCID

Abstract

AbstractWe establish a general version of Cauchy’s integral formula and a residue theorem for polar-analytic functions, employing the new notion of logarithmic poles. As an application, a Boas-type differentiation formula in Mellin setting and a Bernstein-type inequality for polar Mellin derivatives are deduced.

Funder

Friedrich-Alexander-Universität Erlangen-Nürnberg

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s40574-020-00226-9.pdf

Reference9 articles.

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2. Bardaro, C., Butzer, P.L., Mantellini, I., Schmeisser, G.: Quadrature formulae for the positive real axis in the setting of Mellin analysis: sharp error estimates in terms of the Mellin distance. Calcolo 55(3), article 26 (2018)

3. Bardaro, C., Butzer, P.L., Mantellini, I., Schmeisser, G.: Development of a new concept of polar analytic functions useful in Mellin analysis. Complex Var. Ellptic Eq. 64(12), 2040–2062 (2019)