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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
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1997, Volume 61, Issue 3, Pages 133–158
DOI: https://doi.org/10.4213/im128
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. RAN. Ser. Mat., 61:3 (1997), 133–158; Izv. Math., 61:3 (1997), 593–618
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v61/i3/p133
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:252
    English version PDF:6
    References:64
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