Implicit linear difference equation in Frechet spaces
DOI:
https://doi.org/10.15407/dopovidi2017.06.003Keywords:
Frechet space, implicit difference equationAbstract
An criterion of the existence and the uniqueness for a solution of the implicit linear difference equation Axn+1+Bxn=gn, 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
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