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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
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
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
Linking options:
https://www.mathnet.ru/eng/im128https://doi.org/10.1070/im1997v061n03ABEH000128 https://www.mathnet.ru/eng/im/v61/i3/p133
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Abstract page: | 325 | Russian version PDF: | 252 | English version PDF: | 6 | References: | 64 | First page: | 1 |
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