Differentiable, Holomorphic, and Analytic Functions on Complex Φ-Algebras

2022/11/25 by Mark Roelands, Roelands, Mark, Christopher Schwanke +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Polynomial and algebraic computation #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2211.14081

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.

Cited by

• Classical theorems from analysis for locally band preserving functions on Dedekind complete Φ-algebras

Related

• Series and power series on universally complete complex vector lattices
• Analytic cliffordian functions
• Notes on algebras and vector spaces of functions
• Topics in global real analytic geometry
• Classical theorems from analysis for locally band preserving functions on Dedekind complete Φ-algebras