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

Bardaro C, Butzer PL, Mantellini I, Schmeißer G (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Complex Variables and Elliptic Equations Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis

DOI: 10.1080/17476933.2019.1571050

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.

Authors with CRIS profile

Gerhard Schmeißer Department Mathematik

Involved external institutions

Università degli Studi di Perugia

Italy (IT) Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen

Germany (DE)

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: Download