English

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

Complex Variables 2018-05-04 v2

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.

Keywords

Cite

@article{arxiv.1803.04258,
  title  = {Development of a complex function theory upon a new concept of polar-analytic functions; Extended version},
  author = {Carlo Bardaro and Paul. L. Butzer and Ilaria Mantellini and Gerhard Schmeisser},
  journal= {arXiv preprint arXiv:1803.04258},
  year   = {2018}
}

Comments

14 pages, 3 figures. arXiv admin note: text overlap with arXiv:1706.00285

R2 v1 2026-06-23T00:49:45.178Z