Induced representations and a new proof of the imprimitivity theorem

DOI10.1016/0022-1236(79)90009-0zbMath0402.22004OpenAlexW2029002823MaRDI QIDQ1255588

Bent Orsted

Publication date: 1979

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(79)90009-0

zbMATH Keywords

Group RepresentationsHarmonic AnalysisLocally Compact GroupTopological GroupsImprimitivity Theorem

Mathematics Subject Classification ID

Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Induced representations for locally compact groups (22D30)

Related Items (22)

Square-integrability modulo a subgroup ⋮ Gruppentheoretische aspekte der signalübertragung und der kardinalen interpolationssplines I ⋮ Harmonic analysis on tori ⋮ An imprimitivity theorem for hypergroups ⋮ Induced representations of nonlocally compact groups ⋮ Spectral transform for the sub-Laplacian on the Heisenberg group ⋮ Von Neumann indices and classes of positive definite functions ⋮ On quotient measures and induced representations ⋮ Partial differential operators and discrete subgroups of a Lie group ⋮ Systems of covariance and subrepresentations of induced representations ⋮ Self adjoint extensions satisfying the Weyl operator commutation relations ⋮ Second-order right-invariant partial differential equations on a Lie group ⋮ Spectral theory of finite volume domains in \(R^ n\). ⋮ A generalization to locally compact Abelian groups of a spectral problem for commuting partial differential operators ⋮ Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure ⋮ Quantum time delay for unitary operators: General theory ⋮ Spectral and scattering properties of quantum walks on homogenous trees of odd degree ⋮ Positive elements in the algebra of the quantum moment problem ⋮ Lie groupoids and Lie algebroids in physics and noncommutative geometry ⋮ Cyclic vectors for Hilbert algebras ⋮ Dilations of symmetric operators shifted by a unitary group ⋮ Harmonic Analysis of Fractal Processes via C * - Algebras

Cites Work

• Positive definite functions and induced representations
• Induced representations of C\(^*\)-algebras
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Positive Definite Measures
• On a theorem of G. W. Mackey
• Imprimitivity for Representations of Locally Compact Groups I

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