Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-note-on-continuous-stable-sampling-4l70dskgdp
References (26)
-
Zhong-Qi Xiang (2013)
New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous FramesAdvances in Mathematical Physics, 2013
-
G. Murphy (1990)
C*-Algebras and Operator Theory -
O. Christensen (2002)
An introduction to frames and Riesz bases -
A. Ron (2005)
Review of An introduction to Frames and Riesz bases, applied and numerical Harmonic analysis by Ole Christensen Birkhäuser, Basel, 2003Journal of Approximation Theory, 134
-
W. Kilmer (1998)
A Friendly Guide To WaveletsProceedings of the IEEE, 86
-
B. Torrésani (1991)
Wavelets associated with representations of the affine Weyl–Heisenberg groupJournal of Mathematical Physics, 32
-
G. Folland (1995)
A course in abstract harmonic analysis -
Antonio Garc'ia, Miguel Hern'andez-Medina, Gerardo P'erez-Villal'on (2019)
Convolution Systems on Discrete Abelian Groups as a Unifying Strategy in Sampling TheoryResults in Mathematics, 75
-
Syed Ali, J. Antoine, J. Gazeau (2013)
Coherent States, Wavelets, and Their Generalizations -
R. Gol, R. Tousi (2008)
The structure of shift invariant spaces on a locally compact abelian groupJournal of Mathematical Analysis and Applications, 340
-
P. Balázs, Dominik Bayer, A. Rahimi (2011)
Multipliers for continuous frames in Hilbert spacesJournal of Physics A: Mathematical and Theoretical, 45
-
P. Aniello, G. Cassinelli, E. Vito, A. Levrero (1998)
Square-Integrability of Induced Representations of Semidirect ProductsReviews in Mathematical Physics, 10
-
D. Freeman, D. Speegle (2016)
The discretization problem for continuous framesAdvances in Mathematics
-
B. Torrésani (1995)
Position-frequency analyis for signals defined on spheresSignal Process., 43
-
M. Fornasier (2004)
Banach frames for alpha-modulation spacesarXiv: Functional Analysis
-
M. Fornasier, H. Rauhut (2004)
Continuous Frames, Function Spaces, and the Discretization ProblemJournal of Fourier Analysis and Applications, 11
-
A. García, M. Hernández-Medina, G. Pérez-Villalón (2016)
Sampling in Unitary Invariant Subspaces Associated to LCA GroupsResults in Mathematics, 72
-
Ali, J. Antoine, J. Gazeau, U. Mueller (1995)
Coherent states and their generalizations - A mathematical overviewReviews in Mathematical Physics, 7
-
I. Bogdanova, P. Vandergheynst, J. Antoine, L. Jacques, M. Morvidone (2005)
Stereographic wavelet frames on the sphereApplied and Computational Harmonic Analysis, 19
-
A. Rahimi, A. Najati, Y. Dehghan (2006)
CONTINUOUS FRAMES IN HILBERT SPACES, 12
-
H. Führ (2005)
Abstract Harmonic Analysis of Continuous Wavelet Transforms -
Syed Ali, J. Antoine, J. Gazeau (1993)
Continuous Frames in Hilbert SpaceAnnals of Physics, 222
-
M. Fornasier (2007)
Banach frames for α-modulation spacesApplied and Computational Harmonic Analysis, 22
-
Mads Jakobsen, J. Lemvig (2014)
Reproducing formulas for generalized translation invariant systems on locally compact abelian groupsTransactions of the American Mathematical Society, 368
-
P. Aniello (2003)
Square integrable projective representations and square integrable representations modulo a relatively central subgroup (I): basic resultsarXiv: Quantum Physics
-
J. Gabardo, D. Han (2003)
Frames Associated with Measurable SpacesAdvances in Computational Mathematics, 18
- Publisher
- Springer Journals
- Copyright
- Copyright © Tusi Mathematical Research Group (TMRG) 2020
- ISSN
- 2662-2009
- eISSN
- 2538-225X
- DOI
- 10.1007/s43036-020-00061-x
- Publisher site
- See Article on Publisher Site
Abstract
As a starting point we assume to have a continuous frame in a Hilbert space with respect to a measure space. This frame inherits a unitary structure from a unitary representation of a locally compact abelian group in the Hilbert space. In this setting we state a continuous sampling result for the range space of the associated analysis frame operator. The data sampling are functions also defined by using the underlying unitary structure. The result is illustrated by using continuous frames in Paley–Wiener and shift-invariant spaces generated by translates of fixed functions. A sampling strategy working only for discrete abelian groups is also discussed.
Journal
Advances in Operator Theory – Springer Journals
Published: Jul 14, 2020