The matrix-valued Riesz lemma and local orthonormal bases in shift-invariant spaces

DOI10.1023/A:1027389826705zbMath1036.42035OpenAlexW2165783715MaRDI QIDQ1424937

Thomas A. Hogan, Douglas P. Hardin, Qiyu Sun

Publication date: 15 March 2004

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1027389826705

zbMATH Keywords

waveletsshift-invariant spaceorthogonal basesmultiresolutionframeFejér-Riesz lemma

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Factorization of matrices (15A23) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68)

Related Items (14)

Affine frame decompositions and shift-invariant spaces ⋮ Factorization of multivariate positive Laurent polynomials ⋮ Rank-deficient spectral factorization and wavelets completion problem ⋮ Extension of Shift-Invariant Systems inL²(ℝ) to Frames ⋮ Generalized matrix spectral factorization with symmetry and applications to symmetric quasi-tight framelets ⋮ Bauer's spectral factorization method for low order multiwavelet filter design ⋮ Generalized matrix spectral factorization and quasi-tight framelets with a minimum number of generators ⋮ Matrix spectral factorization and wavelets ⋮ Tight wavelet frames via semi-definite programming ⋮ Matrix splitting with symmetry and dyadic framelet filter banks over algebraic number fields ⋮ Symmetric tight wavelet frames with rational coefficients ⋮ An algebraic perspective on multivariate tight wavelet frames. II ⋮ A simple proof of the matrix-valued Fejér--Riesz theorem ⋮ Matrix spectral factorization for SA4 multiwavelet

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