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Continuation of multiple power series in a sectorial domain
Author(s) -
Mkrtchyan A. J.
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.201900042
Subject(s) - mathematics , holomorphic function , series (stratigraphy) , power series , continuation , domain (mathematical analysis) , variable (mathematics) , analytic continuation , function series , function (biology) , formal power series , power (physics) , mathematical analysis , computer science , paleontology , physics , quantum mechanics , programming language , evolutionary biology , biology
For multiple power series centered at the origin we consider the problem of its analytic continuability into a sectorial domain. The condition for continuability is formulated in terms of a holomorphic function that interpolates the series coefficients. For series in one variable this problem has been studied in the works of E. Lindelöf, N. Arakelian, and others.