Wavelets on the n-sphere and related manifolds

DOI10.1063/1.532481zbMath0929.42029OpenAlexW2063616966MaRDI QIDQ4701632

Jean-Pierre Antoine, Pierre Vandergheynst

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532481

zbMATH Keywords

representationsRiemannian symmetric spacesgeneralized Lorentz groupgroup-theoretical derivation of the continuous wavelet transform

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Coherent states (81R30) Structure and representation of the Lorentz group (22E43) Differential geometry of symmetric spaces (53C35)

Related Items (35)

Sparse representation on graphs by tight wavelet frames and applications ⋮ On some nonlinear nonisotropic quasi-self-similar functions ⋮ Separable projection integrals for higher-order correlators of the cosmic microwave sky: acceleration by factors exceeding 100 ⋮ Wavelet transform on the circle and the real line: a unified group-theoretical treatment ⋮ Continuous wavelets on compact manifolds ⋮ Localisation of directional scale-discretised wavelets on the sphere ⋮ Continuous wavelet frames on the sphere: the group-theoretic approach revisited ⋮ Wavelet based solutions to the Poisson and the Helmholtz equations on the \(n\)-dimensional unit sphere ⋮ Spherical Framelets from Spherical Designs ⋮ THE CONTINUOUS WAVELET TRANSFORM ON CONIC SECTIONS ⋮ Orthogonal Wavelet Frames on Manifolds Based on Conformal Mappings ⋮ Spherical fast multiscale approximation by locally compact orthogonal wavelets ⋮ Wavelet transform on the torus: a group theoretical approach ⋮ Continuous wavelet transforms on the space \(L^{2}(\mathbf R,\mathbb H; dx)\) ⋮ Approximation of the differential operators on an adaptive spherical geodesic grid using spherical wavelets ⋮ ON THE UNCERTAINTY PRODUCT OF SPHERICAL WAVELETS ⋮ LOCAL WAVELET TRANSFORM ON THE SMOOTH SURFACE OF ROTATION CLASS ⋮ Extended MacMahon-Schwinger's master theorem and conformal wavelets in complex Minkowski space ⋮ Wavelet transform on manifolds: old and new approaches ⋮ Frames of Poisson wavelets on the sphere ⋮ Wavelets onS³andSO(3)-Their construction, relation to each other and Radon transform of wavelets onSO(3) ⋮ Tight framelets and fast framelet filter bank transforms on manifolds ⋮ Biorthogonal radial multiresolution in dimension three ⋮ Continuous wavelet transforms on \(n\)-dimensional spheres ⋮ Spherical continuous wavelet transforms arising from sections of the Lorentz group ⋮ On the diffusion equation and diffusion wavelets on flat cylinders and the n-torus ⋮ Wavelets on the 2-sphere: A group-theoretical approach ⋮ Spin weighted spherical wavelets derived from approximate identities ⋮ Marcinkiewicz averages of smooth orthogonal projections on sphere ⋮ A continuous spherical wavelet transform for \(\mathcal{C}(\mathcal{S}^n)\) ⋮ Characterizations of function spaces on the sphere using frames ⋮ Wavelets on the 2-sphere and related manifolds ⋮ CONSTRUCTION OF THE MULTI-WAVELETS ON SOME SMOOTH PLANE CURVES VIA LENGTH-PRESERVING PROJECTION ⋮ Wavelets on the sphere: implementation and approximations ⋮ Semi-continuous and discrete wavelet frames on \(n\)-dimensional spheres

Cites Work

• Position-frequency analysis for signals defined on spheres
• Combined spherical harmonic and wavelet expansion -- a future concept in earth's gravitational determination
• Admissible wavelets associated with the affine automorphism group of the Siegel upper half-plane
• Image analysis with two-dimensional continuous wavelet transform
• Admissible wavelets associated with the Heisenberg group
• The lifting scheme: A custom-design construction of biorthogonal wavelets
• Wavelet transforms associated to a principal series representation of semisimple Lie groups. II
• Contractions of representations of de Sitter groups
• Coherent states for arbitrary Lie group
• Nonstationary wavelets on the \(m\)-sphere for scattered data
• Contraction of Lie Groups
• Wavelet analysis on the circle
• Transforms associated to square integrable group representations. I. General results
• Painless nonorthogonal expansions
• Multiresolution analysis and wavelets onS²andS³
• COHERENT STATES AND THEIR GENERALIZATIONS: A MATHEMATICAL OVERVIEW
• Continuous wavelet transforms on the sphere
• On the Contraction of Groups and Their Representations

This page was built for publication: Wavelets on the n-sphere and related manifolds