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Izvestiya: Mathematics, 1997, Volume 61, Issue 3, Pages 593–618
DOI: https://doi.org/10.1070/im1997v061n03ABEH000128 (Mi im128) 		 
Conditions for the range of a difference operator to be closed

S. G. Merzlyakov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
English version PDF (222 kB) Russian version article
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DOI: https://doi.org/10.1070/im1997v061n03ABEH000128
Abstract: In this paper we study difference operators with variable differences that lie on a straight line in the space of holomorphic functions of a single variable. We obtain necessary and sufficient conditions for the range of such operators to be closed in terms of the zeros of their extreme coefficients. For a wide class of regions these conditions give simple criteria for the range of a difference operator to be closed.
Received: 29.08.1995
Bibliographic databases:
MSC: Primary 47B38; Secondary 30H05, 39A70
Language: English
Original paper language: Russian
Citation: S. G. Merzlyakov, “Conditions for the range of a difference operator to be closed”, Izv. Math., 61:3 (1997), 593–618
Citation in format AMSBIB
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\by S.~G.~Merzlyakov
\paper Conditions for the range of a~difference operator to be closed
\jour Izv. Math.
\yr 1997
\vol 61
\issue 3
\pages 593--618
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