Abstract
We establish a criterion for the existence and uniqueness of solutions of a linear difference equation with an unbounded operator coefficient belonging to the space l p(B) of sequences of elements of a Banach space B.
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REFERENCES
A. G. Baskakov, “On conditions for the invertibility and Fredholm property of difference operators,” Dokl. Akad. Nauk Rossii, 372, No. 3, 309–310 (2000).
A. Ya. Dorogovtsev,Periodic and Stationary Modes of Infinite-Dimensional Deterministic and Stochastic Dynamical Systems [in Russian], Vyshcha Shkola, Kiev (1992).
M. F. Gorodnii, “Bounded and periodic solutions of one difference equation and its stochastic analog in a Banach space,” Ukr. Mat. Zh., 43, No. 1, 41–46 (1991).
A. A. Kirillov and A. D. Gvishiani, Theorems and Problems of Functional Analysis [in Russian], Nauka, Moscow (1979).
E. Hille and R. Phillips, Functional Analysis and Semigroups [Russian translation], Izd. Inostran. Liter., Moscow (1962).
D. Henry, Geometric Theory of Semilinear Parabolic Equations [Russian translation], Mir, Moscow (1985).
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Gorodnii, M.F. l p-Solutions of One Difference Equation in a Banach Space. Ukrainian Mathematical Journal 55, 512–519 (2003). https://doi.org/10.1023/A:1025885529972
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DOI: https://doi.org/10.1023/A:1025885529972