The compactness principle and Vitaliʼs theorem for h-holomorphic functions

Abstract

In this paper, we consider the properties of uniformly convergent sequences of h-holomorphic functions on the set of h-complex numbers. Theorems on the global antiderivative and on the uniform approximation of h-holomorphic functions by polynomials are formulated and proven. The sufficient conditions for the h-holomorphism of the limit function are obtained. The compactness principle for functions of an h-complex variable and an analog of Vitaliʼs theorem for h-analytic functions are formulated and proven.