The density theorem for operator-valued frames via square-integrable representations of locally compact groups

DOI10.1007/S00041-024-10107-WMaRDI QIDQ6632421

Pengtong Li, Jingsheng Wang, Deguang Han

Publication date: 4 November 2024

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

wavelet transformlocally compact groupdensity theoremoperator-valued frameHilbert-Schmidt operator

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) General harmonic expansions, frames (42C15) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Representation theory of groups (20C99) Analysis on specific locally compact and other abelian groups (43A70)

Cites Work

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• Density and duality theorems for regular Gabor frames
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• Subspaces of \(L^2(G)\) invariant under translation by an abelian subgroup
• History and evolution of the density theorem for Gabor frames
• Continuous wavelet frames on the sphere: the group-theoretic approach revisited
• The density theorem for projective representations via twisted group von Neumann algebras
• The density theorem for discrete series representations restricted to lattices
• Operator-valued frames
• The Γ-equivariant form of the Berezin quantization of the upper half plane
• Frames, bases and group representations
• An introduction to frames and Riesz bases

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