A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS

DOI10.1142/S0219691310003365zbMath1188.43002OpenAlexW4250772064WikidataQ120862303 ScholiaQ120862303MaRDI QIDQ5305114

Rajab Ali Kamyabi-Gol, Reihaneh Raisi Tousi

Publication date: 19 March 2010

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219691310003365

zbMATH Keywords

waveletsshift-invariant spaceframelocally compact abelian grouprange function

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items

Unnamed Item ⋮ Some equivalent multiresolution conditions on locally compact Abelian groups ⋮ Frames generated by compact group actions ⋮ Modulation preserving operators on locally compact abelian groups ⋮ The structure of translation-invariant spaces on locally compact abelian groups ⋮ Rationally sampled Gabor frames on the half real line ⋮ Modulation invariant spaces on locally compact abelian groups ⋮ Multiplication-invariant operators and the classification of LCA group frames ⋮ SHIFT INVARIANT SPACES FOR LOCAL FIELDS ⋮ Translation preserving operators on locally compact abelian groups ⋮ Linear combinations of generators in multiplicatively invariant spaces ⋮ Subspaces of \(L^2(G)\) invariant under translation by an abelian subgroup ⋮ The Zak transform and the structure of spaces invariant by the action of an LCA group

Cites Work

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• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
• Abstract harmonic analysis of continuous wavelet transforms
• The structure of shift invariant spaces on a locally compact abelian group
• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)