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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 21
  3. Journal of Fourier Analysis and Applications : Volume 21, Issue 6, December 2015
  4. Operator-Valued Frames for the Heisenberg Group
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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 21
Journal of Fourier Analysis and Applications : Volume 21, Issue 6, December 2015
Ambiguities in One-Dimensional Discrete Phase Retrieval from Fourier Magnitudes
Uncertainty Principles and Light Cones
Phase Retrieval for the Cauchy Wavelet Transform
Group Algebras Acting on $$L^p$$ -Spaces
Frame Potentials and the Geometry of Frames
Operator-Valued Frames for the Heisenberg Group
Journal of Fourier Analysis and Applications : Volume 21, Issue 5, October 2015
Journal of Fourier Analysis and Applications : Volume 21, Issue 4, August 2015
Journal of Fourier Analysis and Applications : Volume 21, Issue 3, June 2015
Journal of Fourier Analysis and Applications : Volume 21, Issue 2, April 2015
Journal of Fourier Analysis and Applications : Volume 21, Issue 1, February 2015
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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Operator-Valued Frames for the Heisenberg Group

Content Provider SpringerLink
Author Howard, Stephen D. Cochran, Douglas Robinson, Benjamin Moran, William
Copyright Year 2015
Abstract A classical result of Duffin and Schaeffer gives conditions under which a discrete collection of characters on $${\mathbb {R}}$$ , restricted to $$E=(-\gamma ,\gamma )\subsetneq (-1/2,1/2)$$ , forms a Hilbert-space frame for $$L^2(E)$$ . For the case of characters with period one, this is just the Poisson Summation Formula. Duffin and Schaeffer show that perturbations preserve the frame condition in this case. This paper gives analogous results for the real Heisenberg group $$H_n$$ , where frames are replaced by operator-valued frames. The Selberg Trace Formula is used to show that perturbations of the orthogonal case continue to behave as operator-valued frames. This technique enables the construction of decompositions of elements of $$L^2(E)$$ for suitable subsets $$E$$ of $$H_n$$ in terms of representations of $$H_n$$ .
Ending Page 1397
Page Count 14
Starting Page 1384
File Format PDF
ISSN 10695869
e-ISSN 15315851
Journal Journal of Fourier Analysis and Applications
Issue Number 6
Volume Number 21
Language English
Publisher Springer US
Publisher Date 2015-05-06
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Abstract Harmonic Analysis G-frames Mathematical Methods in Physics Operator-valued frames Heisenberg Group Fourier Analysis Signal, Image and Speech Processing Approximations and Expansions Representations General harmonic expansions, frames Sampling Partial Differential Equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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