Geometric aspects of frame representations of abelian groups

DOI10.1090/S0002-9947-04-03679-7zbMath1054.43008arXivmath/0308250MaRDI QIDQ4811899

David R. Larson, Eric S. Weber, Wai-Shing Tang, Akram Al-Droubi

Publication date: 6 September 2004

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

Full work available at URL: https://arxiv.org/abs/math/0308250

zbMATH Keywords

waveletlocally compact abelian groupspectral multiplicityWeyl-Heisenberg framemultiplexingregular samplingperiodic samplingframe representation

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sampling theory in information and communication theory (94A20) Spectral synthesis on groups, semigroups, etc. (43A45) Miscellaneous applications of functional analysis (46N99) Analysis on specific locally compact and other abelian groups (43A70)

Related Items

Frame vectors for representations of abelian groups ⋮ Frames and bases in tensor products of Hilbert spaces and Hilbert \(C^*\)-modules ⋮ Frame representations and Parseval duals with applications to Gabor frames ⋮ Linearly connected sequences and spectrally optimal dual frames for erasures ⋮ Measure functions for frames ⋮ Localized bases in \(L^2(0,1)\) and their use in the analysis of Brownian motion ⋮ Hilbert spaces of martingales supporting certain substitution-dynamical systems ⋮ The existence of tight Gabor duals for Gabor frames and subspace Gabor frames ⋮ Parseval frames for ICC groups ⋮ Wavelet frames for (not necessarily reducing) affine subspaces ⋮ Orthogonal frames of translates ⋮ On the orthogonality of frames and the density and connectivity of wavelet frames ⋮ Iterated function systems, Ruelle operators, and invariant projective measures

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