Admissible vectors for the regular representation

DOI10.1090/S0002-9939-02-06433-XzbMath1002.43004arXivmath/0010051OpenAlexW2118919204MaRDI QIDQ4536059

Hartmut Führ

Publication date: 17 June 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010051

zbMATH Keywords

locally compact groupcoherent statessquare-integrable representationswavelet transformscyclic vectorsPlancherel theorycontinuous wavelet transforms

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items (6)

Unnamed Item ⋮ Square-integrability modulo a subgroup ⋮ Characterization of regularity for a connected abelian action ⋮ The density theorem for discrete series representations restricted to lattices ⋮ The continuous Zak transform and generalized Gabor frames ⋮ Groups with frames of translates

Cites Work

• Group representations in reproducing kernel Hilbert spaces
• On the regular representation of a nonunimodular locally compact group
• Plancherel inversion as unified approach to wavelet transforms and Wigner functions
• A characterization of the higher dimensional groups associated with continuous wavelets.
• Continuous wavelet transforms from semidirect products: cyclic representations and Plancherel measure.
• Coherent states, wavelets and their generalizations
• Plancherel formula for non-unimodular locally compact groups
• Q.U.P. and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups
• Borel Structure in Groups and Their Duals
• A wavelet transform for the Poincaré group
• Transforms associated to square integrable group representations. I. General results
• Coherent states for n-dimensional Euclidean groups E(n) and their application
• Wavelet transform and orthogonal decomposition of space 𝐿² on the Cartan domain 𝐵𝐷𝐼(𝑞=2)
• Wavelets from Square-Integrable Representations
• Wavelet frames and admissibility in higher dimensions
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