Spectral Theorem for Unbounded Strongly Continuous Groups on a Hilbert Space

DOI10.2307/2160176zbMath0820.47017OpenAlexW4250548536MaRDI QIDQ4281746

Khristo N. Boyadzhiev, Ralph J. De Laubenfels

Publication date: 10 March 1994

Full work available at URL: https://doi.org/10.2307/2160176

zbMATH Keywords

functional calculusspectral theoremstrongly continuous group of operators of exponential type

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Functional calculus for linear operators (47A60) Spectrum, resolvent (47A10) Groups and semigroups of linear operators (47D03) Functional calculus in topological algebras (46H30)

Related Items

A transference principle for general groups and functional calculus on UMD spaces ⋮ Hardy inequality and the construction of infinitesimal operators with non-basis family of eigenvectors ⋮ Quasi-distribution semigroups and integrated semigroups ⋮ Operational calculus and integral transforms for groups with finite propagation speed ⋮ Bounded \(H ^{\infty }\)-calculus for strip-type operators ⋮ Functional calculus and dilation for \(C_{0}\)-groups of polynomial growth ⋮ Functional calculus for semigroup generators via transference ⋮ Transference principles for semigroups and a theorem of Peller ⋮ \(H ^{\infty }\)-functional calculus and models of Nagy-Foiaş type for sectorial operators ⋮ A semigroup approach to fractional powers ⋮ One-parameter groups of regular quasimultipliers ⋮ CHARACTERIZATIONS OF THE SERIES GROUP GENERATORS ON HILBERT SPACES AND THE H^{\infty}-CALCULUS ⋮ Similarity to a contraction, for power-bounded operators with finite peripheral spectrum ⋮ AN UNBOUNDED OPERATOR WITH SPECTRUM IN A STRIP AND MATRIX DIFFERENTIAL OPERATORS

Cites Work

• Some results about complex powers of closed operators
• Spectral properties of the Laplace operator in \(L^ p(R)\)
• Applications of the purely imaginary powers of operators in Hilbert spaces
• On operators with bounded imaginary powers in Banach spaces
• Examples of unbounded imaginary powers of operators
• Semigroups and resolvents of bounded variation imaginary powers and \(H^ \infty\) functional calculus
• Analytic generators for one-parameter groups
• Spectral distributions and generalization of Stone's theorem
• On the closedness of the sum of two closed operators
• Unbounded holomorphic functional calculus and abstract Cauchy problems for operators with polynomially bounded resolvents
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item