Infinite convolution products and refinable distributions on Lie groups

DOI10.1090/S0002-9947-00-02409-0zbMath0940.43002WikidataQ115289165 ScholiaQ115289165MaRDI QIDQ4955716

Wayne M. Lawton

Publication date: 22 May 2000

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

zbMATH Keywords

Riesz basisdistributionLie groupdilationenveloping algebratransition operatorrefinement operatorcascade sequence

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Measures on groups and semigroups, etc. (43A05) Spline approximation (41A15) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (7)

Autosimilar Lévy processes on Lie groups ⋮ Shannon multiresolution analysis on the Heisenberg group ⋮ Lipschitz continuity of refinable functions on the Heisenberg group ⋮ On an infinite convolution product of measures ⋮ Convergence of cascade sequence on the Heisenberg group ⋮ MULTIRESOLUTION ANALYSIS AND HAAR WAVELETS ON THE PRODUCT OF HEISENBERG GROUP ⋮ Multiresolution analysis and Haar wavelets on the Laguerre hypergroup

Cites Work

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• Lie groups and algebras with applications to physics, geometry, and mechanics
• Notes on Lie algebras.
• A stability criterion for biorthogonal wavelet bases and their related subband coding scheme
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Convergence of multidimensional cascade algorithm
• General existence theorems for orthonormal wavelets, an abstract approach
• Subdivision schemes in \(L_ p\) spaces
• Biorthogonal wavelet bases on \(\mathbb{R}^ d\)
• Analysis of uniform binary subdivision schemes for curve design
• Derivations of Nilpotent Lie Algebras
• Multiresolution properties of the wavelet Galerkin operator
• Tight frames of compactly supported affine wavelets
• Base d'ondelettes sur les groupes de Lie stratifiés
• Orthonormal bases of compactly supported wavelets
• Necessary and sufficient conditions for constructing orthonormal wavelet bases
• Stationary subdivision
• Harmonic Analysis in Phase Space. (AM-122)
• Ten Lectures on Wavelets
• Energy Moments in Time and Frequency for Two-Scale Difference Equation Solutions and Wavelets
• Sobolev Characterization of Solutions of Dilation Equations
• Biorthogonal bases of compactly supported wavelets
• Wandering vectors for unitary systems and orthogonal wavelets
• Multiresolution and wavelets
• Stability and Orthonormality of Multivariate Refinable Functions
• Refinable Function Vectors
• Fourier Analysis of the Finite Element Method in Ritz‐Galerkin Theory
• A nilpotent Lie algebra with nilpotent automorphism group
• Introduction to Lie Algebras and Representation Theory
• A Note on Automorphisms and Derivations of Lie Algebras
• Produits tensoriels topologiques et espaces nucléaires

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