Differentiable, holomorphic, and analytic functions on complex Φ-algebras

Journal of Mathematical Analysis and Applications, vol. 541, pp. 128671

Abstract

Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex Φ-algebras. Most notably, we improve the Cauchy-Hadamard formulas for universally complete complex vector lattices given by both authors in a previous paper in order to prove that analytic functions are holomorphic in this abstract setting.

Authors 2

1. Mark C. P. Roelands Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, 2300 RA Leiden, the Netherlands

2. Christopher Schwanke corresponding

   University of Pretoria

   Affiliation as printed

   Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa