Weak frames in Hilbert \(C^*\)-modules with application in Gabor analysis

DOI10.1215/17358787-2019-0021zbMath1434.42041arXiv1903.01952OpenAlexW2918600833MaRDI QIDQ2329258

Damir Bakić

Publication date: 17 October 2019

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.01952

zbMATH Keywords

von Neumann algebraBessel sequenceframeGabor frameHilbert \(C^\ast\)-module

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) (C^*)-modules (46L08) General theory of von Neumann algebras (46L10) General harmonic expansions, frames (42C15)

Related Items (2)

Topological and frame properties of certain pathological \(C^{\ast}\)-algebras ⋮ Modular Riesz bases versus Riesz bases in Hilbert C∗-modules

Cites Work

• The mystery of Gabor frames
• A basis theory primer.
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• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• Weyl-Heisenberg frames and Riesz bases in \(L_2(\mathbb{R}^d)\)
• Foundations of time-frequency analysis
• Self-duality and \(C^*\)-reflexivity of Hilbert \(C^*\)-moduli
• Validity of WH-frame bound conditions depends on lattice parameters
• Frames and outer frames for Hilbert -modules
• Projections in noncommutative tori and Gabor frames
• On frames for countably generated Hilbert 𝐶*-modules
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Hilbert 𝐶*-modules in which all closed submodules are complemented
• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)
• Sampling and periodization of generators of Heisenberg modules
• Inner Product Modules Over B ∗ -Algebras
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• Weyl-Heisenberg frames, translation invariant systems and the Walnut representation
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