An abstract interpretation of the wavelet dimension function using group representations

DOI10.1006/jfan.1999.3551zbMath0964.42023OpenAlexW1977271534MaRDI QIDQ1568537

Lawrence W. Baggett

Publication date: 27 August 2000

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3551

zbMATH Keywords

waveletsmultiresolution analysisdimension functiongroup representationmultiwaveletsMRA

Mathematics Subject Classification ID

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

Related Items

The wavelet dimension function is the trace function of a shift-invariant system ⋮ Frame vectors for representations of abelian groups ⋮ Geometric aspects of frame representations of abelian groups ⋮ Frames, modular functions for shift-invariant subspaces and FMRA wavelet frames ⋮ Riesz wavelets and generalized multiresolution analyses. ⋮ Topological and geometric properties of refinable functions and MRA affine frames ⋮ The spectral function of shift-invariant spaces ⋮ A characterization of dimension functions of wavelets ⋮ Minimality of the data in wavelet filters (with an appendix by Brian Treadway) ⋮ A characterization of dimension functions of a class of semi‐orthogonal Parseval frame wavelets ⋮ Dimension functions of rationally dilated GMRAs and wavelets ⋮ Intersection of dilates of shift-invariant spaces ⋮ 𝑊-Markov measures, transfer operators, wavelets and multiresolutions ⋮ Construction and reconstruction of tight framelets and wavelets via matrix mask functions ⋮ Holes in the spectrum of functions generating affine systems ⋮ Minimal generator sets for finitely generated shift-invariant subspaces of \(L^{2}(\mathbb R^{n})\) ⋮ The construction of wavelets from generalized conjugate mirror filters in \(L^2(\mathbb R^n)\)

Cites Work

• Single wavelets in \(n\)-dimensions
• Wavelet sets in \(\mathbb{R}^ n\)
• Smoothing minimally supported frequency wavelets. I
• Generalized multi-resolution analyses and a construction procedure for all wavelet sets in \(\mathbb{R}^n\)
• Ten Lectures on Wavelets
• Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
• Wandering vectors for unitary systems and orthogonal wavelets
• Unnamed Item
• Unnamed Item
• Unnamed Item