Development of a new concept of polar analytic functions useful in Mellin analysis

Journal article


Publication Details

Author(s): Bardaro C, Butzer PL, Mantellini I, Schmeißer G
Journal: Complex Variables and Elliptic Equations
Publication year: 2019
ISSN: 1747-6933


Abstract

In this paper, we develop the concept of polar analyticity introduced in Bardaro C, et al. [A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces. Math Nachr. 2017;290:2759–2774] and successfully applied in Mellin analysis and in quadrature of functions defined on the positive real axis (see Bardaro C, et al. [Quadrature formulae for the positive real axis in the setting of Mellin analysis: sharp error estimates in terms of the Mellin distance]. Calcolo. 2018;55(3):26. Available from: https://doi.org/10.1007/s10092-018-0268-1]). This appears as a simple way to describe functions which are analytic on a part of the Riemann surface of the logarithm. We study analogues of Cauchy's integral theorems for polar-analytic functions and obtain two series expansions in terms of polar-derivatives and Mellin polar-derivatives, respectively. We also describe some geometric properties of polar-analytic functions related to conformality. By these studies, we launch the proposal to develop a complete complex function theory, independent of the classical function theory, which is built upon the new notion of polar analyticity.


FAU Authors / FAU Editors

Schmeißer, Gerhard Prof. Dr.
Department Mathematik


External institutions with authors

Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen
Università degli Studi di Perugia


How to cite

APA:
Bardaro, C., Butzer, P.L., Mantellini, I., & Schmeißer, G. (2019). Development of a new concept of polar analytic functions useful in Mellin analysis. Complex Variables and Elliptic Equations. https://dx.doi.org/10.1080/17476933.2019.1571050

MLA:
Bardaro, Carlo, et al. "Development of a new concept of polar analytic functions useful in Mellin analysis." Complex Variables and Elliptic Equations (2019).

BibTeX: 

Last updated on 2019-06-08 at 21:08