Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-04-03679-7
DC FieldValue
dc.titleGeometric aspects of frame representations of abelian groups
dc.contributor.authorAldroubi, A.
dc.contributor.authorLarson, D.
dc.contributor.authorTang, W.-S.
dc.contributor.authorWeber, E.
dc.date.accessioned2014-10-28T02:36:03Z
dc.date.available2014-10-28T02:36:03Z
dc.date.issued2004-12
dc.identifier.citationAldroubi, A., Larson, D., Tang, W.-S., Weber, E. (2004-12). Geometric aspects of frame representations of abelian groups. Transactions of the American Mathematical Society 356 (12) : 4767-4786. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-04-03679-7
dc.identifier.issn00029947
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/103340
dc.description.abstractWe consider frames arising from the action of a unitary representation of a discrete countable abelian group. We show that the range of the analysis operator can be determined by computing which characters appear in the representation. This allows one to compare the ranges of two such frames, which is useful for determining similarity and also for multiplexing schemes. Our results then partially extend to Bessel sequences arising from the action of the group. We apply the results to sampling on bandlimited functions and to wavelet and Weyl-Heisenberg frames. This yields a sufficient condition for two sampling transforms to have orthogonal ranges, and two analysis operators for wavelet and Weyl-Heisenberg frames to have orthogonal ranges. The sufficient condition is easy to compute in terms of the periodization of the Fourier transform of the frame generators.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1090/S0002-9947-04-03679-7
dc.sourceScopus
dc.subjectFrame representation
dc.subjectLocally compact abelian group
dc.subjectMultiplexing
dc.subjectPeriodic sampling
dc.subjectRegular sampling
dc.subjectSpectral multiplicity
dc.subjectWavelet
dc.subjectWeyl-Heisenberg frame
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1090/S0002-9947-04-03679-7
dc.description.sourcetitleTransactions of the American Mathematical Society
dc.description.volume356
dc.description.issue12
dc.description.page4767-4786
dc.identifier.isiut000223592300004
Appears in Collections:Staff Publications

Show simple item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

18
checked on Sep 17, 2019

WEB OF SCIENCETM
Citations

18
checked on Sep 10, 2019

Page view(s)

51
checked on Sep 7, 2019

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.