Frames of translates for number-theoretic groups

DOI10.1007/s12220-019-00234-yzbMath1468.43003arXiv1804.07783OpenAlexW2963107214WikidataQ127569793 ScholiaQ127569793MaRDI QIDQ2658973

John J. Benedetto, Robert L. Benedetto

Publication date: 25 March 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.07783

zbMATH Keywords

local fieldscompact open subgroupsframes of translatesspectral symbol

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Analysis on specific locally compact and other abelian groups (43A70)

Related Items (3)

Frame of translates and its canonical dual in L2(G) ⋮ Maximal cyclic subspaces for dual integrable representations ⋮ Uniqueness theory for model sets, and spectral superresolution

Cites Work

• The structure of translation-invariant spaces on locally compact abelian groups
• Group Riesz and frame sequences: the bracket and the Gramian
• A wavelet theory for local fields and related groups
• Rates of convergence for the approximation of dual shift-invariant systems in \(\ell^2 (\mathbb{Z})\)
• Shift-invariant spaces on LCA groups
• The Zak transform and the structure of spaces invariant by the action of an LCA group
• The structure of shift invariant spaces on a locally compact abelian group
• Integration and Modern Analysis
• Ten Lectures on Wavelets
• Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform
• Pseudodifferential operators on locally compact abelian groups and Sjöstrand's symbol class
• An introduction to frames and Riesz bases
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