Differentiable, Holomorphic, and Analytic Functions on Complex $\Phi$-Algebras
Functional Analysis
2022-11-28 v1
Abstract
Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex -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.
Cite
@article{arxiv.2211.14081,
title = {Differentiable, Holomorphic, and Analytic Functions on Complex $\Phi$-Algebras},
author = {Mark Roelands and Christopher Michael Schwanke},
journal= {arXiv preprint arXiv:2211.14081},
year = {2022}
}