The spectral function of shift-invariant spaces

DOI10.1307/mmj/1060013204zbMath1059.42021OpenAlexW2130890381MaRDI QIDQ1411315

Ziemowit Rzeszotnik, Marcin Bownik

Publication date: 27 October 2003

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1060013204

zbMATH Keywords

tight framesshift-invariant spacedimension functionspectral functionincompletenessgeneralized multiresolution analysisrange functionmultiplicity functionGarbor systems

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) General harmonic expansions, frames (42C15) Spline approximation (41A15)

Related Items (22)

Density order of Parseval wavelet frames from extension principles ⋮ One-Dimensional Dyadic Wavelets ⋮ Invariance of a shift-invariant space ⋮ The structure of shift-modulation invariant spaces: the rational case ⋮ Closure of dilates of shift-invariant subspaces ⋮ The structure of translation-invariant spaces on locally compact abelian groups ⋮ Cohn-Elkies functions from Gabor frames ⋮ The structure of shift-invariant subspaces of Sobolev spaces ⋮ Modulation invariant spaces on locally compact abelian groups ⋮ On the density order of the principal shift-invariant subspaces of \(L^2(\mathbb R^d)\) ⋮ Linear independence of Parseval wavelets ⋮ A Measurable Selector in Kadison’s Carpenter’s Theorem ⋮ Dyadic bivariate wavelet multipliers in \(L^2(\mathbb R^2)\) ⋮ Lattice invariant subspaces and sampling ⋮ On the existence of multiresolution analysis for framelets ⋮ Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of \(L^2(\mathbb R^d)\) ⋮ Dimension functions of rationally dilated GMRAs and wavelets ⋮ Intersection of dilates of shift-invariant spaces ⋮ Construction and reconstruction of tight framelets and wavelets via matrix mask functions ⋮ Some equations relating multiwavelets and multiscaling functions ⋮ Anisotropic dilations of shift-invariant subspaces and approximation properties in L2(Rd) ⋮ Minimal generator sets for finitely generated shift-invariant subspaces of \(L^{2}(\mathbb R^{n})\)

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