The compactness principle and Vitaliʼs theorem for h-holomorphic functions
https://doi.org/10.29235/1561-2430-2022-58-4-381-388
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.
About the Author
V. A. Pavlovsky
Belarusian State University
Russian Federation
Russian Federation
Vladislav A. Pavlovsky – Postgraduate Student of the Department of Function Theory, Belarusian State University.
4, Nezavisimosti Ave., 220030, Minsk
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