Riesz wavelets and generalized multiresolution analyses.

DOI10.1016/S1063-5203(03)00022-8zbMath1033.42029MaRDI QIDQ1399696

Marcin Bownik

Publication date: 30 July 2003

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

zbMATH Keywords

multiresolution analysisdimension functionshift invariant spacebiorthogonal waveletsMRAgeneralized multiresolution analysisRiesz wavelet

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) General harmonic expansions, frames (42C15)

Related Items (13)

Riesz multiresolution analysis on locally compact abelian groups: construction and exceptions ⋮ The spectral function of shift-invariant spaces ⋮ Unnamed Item ⋮ Characterization of Riesz bases of wavelets generated from multiresolution analysis ⋮ A non-MRA \(c^r\) frame wavelet with rapid decay ⋮ Dimension functions of rationally dilated GMRAs and wavelets ⋮ Intersection of dilates of shift-invariant spaces ⋮ Homogeneous wavelets and framelets with the refinable structure ⋮ On Parseval Wavelet Frames via Multiresolution Analyses in ⋮ Riesz wavelets, tiling and spectral sets in LCA groups ⋮ Holes in the spectrum of functions generating affine systems ⋮ Construction of Parseval wavelets from redundant filter systems ⋮ On Riesz wavelets associated with multiresolution analyses

Cites Work

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• The theory of multiresolution analysis frames and applications to filter banks
• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• An abstract interpretation of the wavelet dimension function using group representations
• The structure of shift-invariant subspaces of \(L^2(\mathbb{R}^n)\)
• On the construction of multivariate (pre)wavelets
• Riesz bases and multiresolution analyses
• The spectral theorem
• On Riesz wavelets associated with multiresolution analyses
• Generalized multi-resolution analyses and a construction procedure for all wavelet sets in \(\mathbb{R}^n\)
• The wavelet dimension function is the trace function of a shift-invariant system
• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)
• A characterization of dimension functions of wavelets
• Characterizations of biorthogonal wavelets which are associated with biorthogonal multiresolution analyses

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