The Cauchy-Pompeiu integral formula in elliptic complex numbers

Abstract

The aim of this article is to give a generalization of the Cauchy-Pompeiu integral formula for functions valued in parameter-depending elliptic algebras with structure polynomial $X^2+\beta X+\alpha$ where $\alpha$ and $\beta$ are real numbers. As a consequence, a Cauchy integral representation formula is obtained for a generalized class of holomorphic functions.

This is a preprint whose final and definitive version has been accepted for publication in Complex Variables and Elliptic Equations

Cited by in corpus (1)

• Operators associated to the Cauchy-Riemann operator in elliptic complex numbers