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The continuous invertibility of functional operators in Banach spaces

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 Abstract: 1. Introduction. This paper is the survey of results on the one- and two-sided (continuous) invertibility for some classes of functional operators in Hölder, Lebesgue and Orlicz spaces, which were obtained in the theory of singular integral operators with discrete groups of shifts. In particular, we consider the invertibility in these spaces for binomial and polynomial operators generated by shift operators, local theory of invertibility in algebras of functional operators with discrete groups of shifts, the solvability of systems of difference equations with incommensurable differences on the semi-axis and finite intervals, and approximation approach to the problem of invertibility of such operators.
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  • Hydroacoustics Branch, Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Soviet Army St. 3, 270100 Odessa, Ukraine
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Bibliografia
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