Tight frame oversampling and its equivalence to shift-invariance of affine frame operators

DOI10.1090/S0002-9939-02-06703-5zbMath1013.42024OpenAlexW1607838410MaRDI QIDQ4791497

Qiyu Sun, Charles K. Chui

Publication date: 28 January 2003

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06703-5

zbMATH Keywords

waveletframeoversamplingwavelet frameshift-invariance

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40)

Related Items (5)

Invariance of a shift-invariant space ⋮ Characterizations of tight over-sampled affine frame systems and over-sampling rates ⋮ Principal shift-invariant spaces with extra invariance nearest to observed data ⋮ Uncertainty principles and Balian-Low type theorems in principal shift-invariant spaces ⋮ Uncertainty principles in finitely generated shift-invariant spaces with additional invariance

Cites Work

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• Bessel sequences and affine frames
• On the translation invariance of wavelet subspaces
• Characterization of general tight wavelet frames with matrix dilations and tightness preserving oversampling
• A characterization of affine dual frames in \(L^2(\mathbb{R}^n)\)
• Oversampling and preservation of tightness in affine frames
• Inequalities on Matrix-Dilated Littlewood--Paley EnergyFunctions and Oversampled Affine Operators
• Wavelets on general lattices, associated with general expanding maps of 𝐑ⁿ
• n × Oversampling Preserves any Tight Affine Frame for Odd n
• Portraits of Frames
• Orthonormal wavelets and tight frames with arbitrary real dilations
• \(p\)-frames and shift invariant subspaces of \(L^p\)
• A characterization of wavelets on general lattices.

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