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

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Details zur Publikation

Autorinnen und Autoren: Bardaro C, Butzer PL, Mantellini I, Schmeißer G
Zeitschrift: Complex Variables and Elliptic Equations
Jahr der Veröffentlichung: 2019
ISSN: 1747-6933


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:]). 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-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Schmeißer, Gerhard Prof. Dr.
Department Mathematik

Einrichtungen weiterer Autorinnen und Autoren

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


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.

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


Zuletzt aktualisiert 2019-06-08 um 21:08