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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2021 Number 8, Pages 37–45 (Mi ivm9701)

This article is cited in 2 papers

Continuation of polyanalytic functions

T. Ishankulova, D. Sh. Fozilovb

a Samarkand State University, 15 University blv., Samarkand, 140104 Uzbekistan
b Samarkand Branch of Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, 47 a Shohruh Mirzo str., Samarkand, 140100 Uzbekistan

Abstract: It is considered the problem of continuation the $n$ analytic function in to a domain by values of its sequential derivatives up to the $(n-1)$-th order on a part of the boundary. It is also considered the problem of inversion of a Cauchy type integral to a Cauchy integral for such functions.

Keywords: Cauchy-Riemann equation, $n$-analytic function, Cauchy theorem, Sokhotskiy-Plemelh formula, continuation formula.

UDC: 517.956

Received: 03.08.2020
Revised: 25.11.2020
Accepted: 24.12.2020

DOI: 10.26907/0021-3446-2021-8-37-45


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, 65:8, 32–39


© Steklov Math. Inst. of RAS, 2024