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On functions with one‐dimensional holomorphic extension property in circular domains
Author(s) -
Kytmanov Alexander M.,
Myslivets Simona G.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800172
Subject(s) - holomorphic function , mathematics , extension (predicate logic) , bounded function , identity theorem , boundary (topology) , domain (mathematical analysis) , property (philosophy) , pure mathematics , analyticity of holomorphic functions , mathematical analysis , computer science , philosophy , epistemology , programming language
In this paper we consider continuous functions given on the boundary of a circular bounded domain D in C n , n > 1 , and having the one‐dimensional holomorphic extension property along family of complex lines, passing through a finite number of points of D . We study the problem of existence of holomorphic extension of such functions into D .