Bounded solutions of a difference equation in Banach space with input data in subspaces
Abstract
UDC 517.929.2
We study the problem of existence and uniqueness of a bounded solution to a difference equation of the first order with a constant operator coefficient in a Banach space. For the case where the initial condition and input sequence are in some subspaces, necessary and sufficient conditions are obtained. These results are applied to difference equations with a jump of operator coefficient and difference equations of higher orders.
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