Holomorphic continuation into a matrix ball of functions defined on a piece of its skeleton
Author:
Khudayberganov G.1,
Abdullayev J.Sh.1
Affiliation:
1. National University of Uzbekistan named after M. Ulugbek
Abstract
The question of the possibility of holomorphic continuation into some domain of functions defined on the entire boundary of this domain has been well studied. The problem of describing functions defined on a part of the boundary that can be extended holomorphically into a fixed domain is attracting more interest. In this article, we reformulate the problem under consideration: Under what conditions can we extend holomorphically to a matrix ball the functions given on a part of its skeleton? We describe the domains into which the integral of the Bochner—Hua Luogeng type for a matrix ball can be extended holomorphically. As the main result, we present the criterion of holomorphic continuation into a matrix ball of functions defined on a part of the skeleton of this matrix ball. The proofs of several results are briefly presented. Some recent advances are highlighted. The results obtained in this article generalize the results of L.A. Aizenberg, A.M. Kytmanov and G. Khudayberganov.
Funder
Ministry of Innovative Development of the Republic of Uzbekistan
Publisher
Udmurt State University
Subject
Fluid Flow and Transfer Processes,General Mathematics,General Computer Science
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献