The spectral theorem

zbMath0615.47021MaRDI QIDQ1820409

Henry Helson

Publication date: 1986

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

positive definitenesscocyclesBochner's theoremWeyl commutation relationStone-von Neumann theoremoperator representationrange functionconstruction of the multiplicity function of a spectral measure in Hilbert spaceinvariant subspaces in the Hardy-Hilbert space

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Groups and semigroups of linear operators (47D03) Research exposition (monographs, survey articles) pertaining to operator theory (47-02)

Related Items (17)

Spectral integrals of Bernoulli generalized functionals ⋮ Frames generated by compact group actions ⋮ The structure of translation-invariant spaces on locally compact abelian groups ⋮ Riesz wavelets and generalized multiresolution analyses. ⋮ The spectral function of shift-invariant spaces ⋮ Modulation invariant spaces on locally compact abelian groups ⋮ Multiplication-invariant operators and the classification of LCA group frames ⋮ A Measurable Selector in Kadison’s Carpenter’s Theorem ⋮ Generalized multi-resolution analyses and a construction procedure for all wavelet sets in \(\mathbb{R}^n\) ⋮ An approximation problem in multiplicatively invariant spaces ⋮ Spectral Types of Uniform Distribution ⋮ Translation preserving operators on locally compact abelian groups ⋮ Phillips symmetric operators and their extensions ⋮ Single generator problem ⋮ Subspaces of \(L^2(G)\) invariant under translation by an abelian subgroup ⋮ The construction of wavelets from generalized conjugate mirror filters in \(L^2(\mathbb R^n)\) ⋮ The Zak transform and the structure of spaces invariant by the action of an LCA group

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