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arXiv · 1803.04258

Development of a complex function theory upon a new concept of polar-analytic functions; Extended version

Carlo Bardaro·Paul. L. Butzer·Ilaria Mantellini·Gerhard Schmeisser
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Abstract

The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature formulae for functions defined on the positive real axis. This appears as a simple way to describe functions which are analytic on a part of the Riemann surface of the logarithm. In this paper we launch a proposal to develop a complete complex function theory, independent of classical function theory, which is built upon the new concept of polar analyticity.

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Carlo Bardaro, Paul. L. Butzer, Ilaria Mantellini, Gerhard Schmeisser. 2018-03-08. Development of a complex function theory upon a new concept of polar-analytic functions; Extended version. https://arxiv.org/abs/1803.04258

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