On local invertibility of functions of an h-complex variable

  • Vladislav A. Pavlovsky Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-2916-1241
  • Igor Leonidovich Vasiliev Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
DOI: https://doi.org/10.33581/2520-6508-2022-1-103-107

Abstract

The theory of functions of an h-complex variable is an alternative to the usual theory of functions of a complex variable, obtained by replacing the rules of multiplication. This change leads to the appearance of zero divisors on the set of h-complex numbers. Such numbers form a commutative ring that is not a field. h-Holomorphic functions are solutions of systems of equations of hyperbolic type, in comparison with classical holomorphic functions, which are solutions of systems of equations of elliptic type. A consequence of this is a significant difference between the properties of h-holomorphic functions and the classical ones. Interest in studying the properties of functions of an h-complex variable is associated with the need to search for new methods for solving problems in mechanics and the plane theory of relativity. The paper presents a theorem on the local invertibility of h-holomorphic functions, formulates the principles of preserving the domain and maximum of the norm.

Author Biographies

Vladislav A. Pavlovsky, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

postgraduate student at the department of function theory, faculty of mechanics and mathematics

Igor Leonidovich Vasiliev, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics), docent; associate professor at the department of function theory, faculty of mechanics and mathematics

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Published
2022-04-01
Keywords: h-holomorphy, local invertibility, domain preservation principle, norm maximum principle, ring of h-complex numbers, zero divisors
How to Cite
Pavlovsky, V. A., & Vasiliev, I. L. (2022). On local invertibility of functions of an h-complex variable. Journal of the Belarusian State University. Mathematics and Informatics, 1, 103-107. https://doi.org/10.33581/2520-6508-2022-1-103-107
Issue
No 1 (2022): Journal of the Belarusian State University. Mathematics and Informatics
Section
Short Communications

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