Spectral Families of Projections, Semigroups, and Differential Operators

DOI10.2307/1999034zbMath0509.47028OpenAlexW4243215934MaRDI QIDQ4747099

T. Alastair Gillespie, Earl Berkson, Harold E. Benzinger

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999034

zbMATH Keywords

strongly continuous semigroupordinary differential operatorsfunctional calculusconditional convergencewell-bounded operatorspectral family of projectionsabstract spectral theorypolar operatorspolar resolvent

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) General theory of ordinary differential operators (47E05) Spectral operators, decomposable operators, well-bounded operators, etc. (47B40) Ordinary differential operators (34L99) Convergence of Fourier series and of inverse transforms (43A50)

Related Items

Fourier series criteria for operator decomposability, Stečkin's theorem, transference, and spectral decompositions, Nonharmonic Fourier Series and Spectral Theory, Spectral Decompositions of One-Parameter Groups of Isometries on Hardy Spaces, Functional calculus for infinitesimal generators of holomorphic semigroups, Spectral decompositions of isometries on \(c_p\), Well-bounded operators on nonreflexive Banach spaces, Functions of Well-Bounded Operators, Spectral decompositions of hyperbolic isometric groups in Hardy spaces of the disk, Periodic groups of operators in Banach spaces, Hilbert, Dirichlet and Fejér families of operators arising from \(C_0\)-groups, cosine functions and holomorphic semigroups, Spectral families of projections in Hardy spaces, Functional calculus for generations of uniformly bounded holomorphic semigroups, On spectral families of projections in Hardy spaces, The existence of spectral decompositions in \(L^ p\)-subspaces, Stone's theorem for strongly continuous groups of isometries in Hardy spaces

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