Abstract
We consider an operator represented by the sum of a series in the values of the resolvent of a densely defined closed operator in a complex Banach space. We describe the left inverse for this operator, apply this result to regularization of equations of the first kind, and consider several examples.
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Notes
This fact contrasts with the approach to solving similar difference equations that is usual for the theory of signal processing (see [17]) where the finiteness requirement for energy is not taken into account.
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Mirotin, A.R. Inversion of Series of Resolvents for Closed Operators and Some Applications. Sib. Adv. Math. 32, 145–156 (2022). https://doi.org/10.1134/S1055134422020079
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DOI: https://doi.org/10.1134/S1055134422020079