Frames and Riesz bases for shift invariant spaces on the abstract Heisenberg group

DOI10.1016/j.indag.2018.09.001zbMath1405.43004OpenAlexW2890368501MaRDI QIDQ1629127

R. Radha, S. Arati

Publication date: 11 December 2018

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2018.09.001

zbMATH Keywords

Riesz basisHeisenberg groupframeslocally compact abelian groupshift invariant spacestwisted translates

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (9)

TWISTED SHIFT-INVARIANT SYSTEM IN ⋮ Systems of left translates and oblique duals on the Heisenberg group ⋮ A study of oblique dual of a system of left translates on the Heisenberg group ⋮ Zak transform associated with the Weyl transform and the system of twisted translates on \(\mathbb{R}^{2n}\) ⋮ Sampling theorem and reconstruction formula for the space of translates on the Heisenberg group ⋮ Shift-invariant system on the Heisenberg group ⋮ Characterizations of woven frames ⋮ Wavelet system and Muckenhoupt $\mathcal {A}_2$ condition on the Heisenberg group ⋮ Hilbert-Schmidt and trace class pseudo-differential operators on the abstract Heisenberg group

Cites Work

• Unnamed Item
• Shift invariant spaces on compact groups
• Characterization of shift-invariant spaces on a class of nilpotent Lie groups with applications
• Frames and Riesz bases of twisted shift-invariant spaces in \(L^2(\mathbb{R}^{2 n})\)
• The structure of translation-invariant spaces on locally compact abelian groups
• The structure of shift-invariant subspaces of \(L^2(\mathbb{R}^n)\)
• Bracket map for the Heisenberg group and the characterization of cyclic subspaces
• Shift-invariant spaces on LCA groups
• A sampling theorem for the twisted shift-invariant space
• The structure of shift invariant spaces on a locally compact abelian group
• Sur certains groupes d'opérateurs unitaires
• Frames and bases. An introductory course
• Harmonic Analysis in Phase Space. (AM-122)
• Zeros of the Zak transform on locally compact abelian groups
• The plancherel formula for group extensions

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