Implicit linear difference equation in Frechet spaces

1Gefter, SL, 1Piven, AL
1V.N. Karazin Kharkiv National University
Dopov. Nac. akad. nauk Ukr. 2017, 6:3-8
Section: Mathematics
Language: Russian
An criterion of the existence and the uniqueness for a solution of the implicit linear difference equation $Ax_{n +1} + Bx_{n} = g_{n}$, where A and B are continuous operators, which act on Frechet spaces, is proved. Explicit formulas for the solution of this equation are found. For the case of Banach spaces, the results are specified.
Keywords: Frechet space, implicit difference equation
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