Spectrum and functions of operators on direct families of Banach spaces
Direct families of Banach spaces, which generalise the notion of direct integrals of Hilbert spaces and the notion of Banach spaces with mixed norms, are considered in this paper. The spectrum, resolvent and analytic functions of bounded linear operators on such direct families of Banach spaces are investigated, and applications to partial integral operators are given. The paper ends with an application to an integrodifferential equation of Barbashin type.
scientific article; zbMATH DE number 5835908