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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 22
  3. Journal of Fourier Analysis and Applications : Volume 22, Issue 6, December 2016
  4. Geometric Space–Frequency Analysis on Manifolds
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Journal of Fourier Analysis and Applications : Volume 23
Journal of Fourier Analysis and Applications : Volume 22
Journal of Fourier Analysis and Applications : Volume 22, Issue 6, December 2016
The Bochner–Schoenberg–Eberlein Property for Totally Ordered Semigroup Algebras
Cartoon Approximation with $$\alpha $$ -Curvelets
Geometric Space–Frequency Analysis on Manifolds
Diagonalization of the Finite Hilbert Transform on Two Adjacent Intervals
Boundedness of Multilinear Pseudo-differential Operators on Modulation Spaces
An $$L^1$$ -Estimate for Certain Spectral Multipliers Associated with the Ornstein–Uhlenbeck Operator
Weak-Type Boundedness of the Hardy–Littlewood Maximal Operator on Weighted Lorentz Spaces
Counterexamples to the B-spline Conjecture for Gabor Frames
Journal of Fourier Analysis and Applications : Volume 22, Issue 5, October 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 4, August 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 3, June 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 2, April 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 1, February 2016
Journal of Fourier Analysis and Applications : Volume 21
Journal of Fourier Analysis and Applications : Volume 20
Journal of Fourier Analysis and Applications : Volume 19
Journal of Fourier Analysis and Applications : Volume 18
Journal of Fourier Analysis and Applications : Volume 17
Journal of Fourier Analysis and Applications : Volume 16
Journal of Fourier Analysis and Applications : Volume 15
Journal of Fourier Analysis and Applications : Volume 14
Journal of Fourier Analysis and Applications : Volume 13
Journal of Fourier Analysis and Applications : Volume 12
Journal of Fourier Analysis and Applications : Volume 11
Journal of Fourier Analysis and Applications : Volume 10
Journal of Fourier Analysis and Applications : Volume 9
Journal of Fourier Analysis and Applications : Volume 8
Journal of Fourier Analysis and Applications : Volume 7
Journal of Fourier Analysis and Applications : Volume 6
Journal of Fourier Analysis and Applications : Volume 5
Journal of Fourier Analysis and Applications : Volume 4
Journal of Fourier Analysis and Applications : Volume 3

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Geometric Space–Frequency Analysis on Manifolds

Content Provider SpringerLink
Author Feichtinger, Hans G. Führ, Hartmut Pesenson, Isaac Z.
Copyright Year 2016
Abstract This paper gives a survey of methods for the construction of space–frequency concentrated frames on Riemannian manifolds with bounded curvature, and the applications of these frames to the analysis of function spaces. In this general context, the notion of frequency is defined using the spectrum of a distinguished differential operator on the manifold, typically the Laplace–Beltrami operator. Our exposition starts with the case of the real line, which serves as motivation and blueprint for the material in the subsequent sections. After the discussion of the real line, our presentation starts out in the most abstract setting proving rather general sampling-type results for appropriately defined Paley–Wiener vectors in Hilbert spaces. These results allow a handy construction of Paley–Wiener frames in $$L_2(\mathbf {M})$$ , for a Riemann manifold of bounded geometry, essentially by taking a partition of unity in frequency domain. The discretization of the associated integral kernels then gives rise to frames consisting of smooth functions in $$L_2(\mathbf {M})$$ , with fast decay in space and frequency. These frames are used to introduce new norms in corresponding Besov spaces on $$\mathbf {M}$$ . For compact Riemannian manifolds the theory extends to $$L_p$$ and associated Besov spaces. Moreover, for compact homogeneous manifolds, one obtains the so-called product property for eigenfunctions of certain operators and proves cubature formulae with positive coefficients which allow to construct Parseval frames that characterize Besov spaces in terms of coefficient decay. The general theory is exemplified with the help of various concrete and relevant examples which include the unit sphere and the Poincaré half plane.
Starting Page 1294
Ending Page 1355
Page Count 62
File Format PDF
ISSN 10695869
Journal Journal of Fourier Analysis and Applications
Volume Number 22
Issue Number 6
e-ISSN 15315851
Language English
Publisher Springer US
Publisher Date 2016-01-25
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Fourier Analysis Signal,Image and Speech Processing Abstract Harmonic Analysis Approximations and Expansions Partial Differential Equations Mathematical Methods in Physics
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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