Publication:
The generalized continuous wavelet transform on Hilbert modules

dc.contributor.advisor Dooley, Anthony en_US
dc.contributor.advisor an Huef, Astrid en_US
dc.contributor.author Ariyani, Ariyani en_US
dc.date.accessioned 2022-03-22T14:45:45Z
dc.date.available 2022-03-22T14:45:45Z
dc.date.issued 2008 en_US
dc.description.abstract The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform. en_US
dc.identifier.uri http://hdl.handle.net/1959.4/42151
dc.language English
dc.language.iso EN en_US
dc.publisher UNSW, Sydney en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/3.0/au/ en_US
dc.subject.other Continuous wavelet transform en_US
dc.subject.other Hilbert C*-Module en_US
dc.title The generalized continuous wavelet transform on Hilbert modules en_US
dc.type Thesis en_US
dcterms.accessRights open access
dcterms.rightsHolder Ariyani, Ariyani
dspace.entity.type Publication en_US
unsw.accessRights.uri https://purl.org/coar/access_right/c_abf2
unsw.identifier.doi https://doi.org/10.26190/unsworks/19618
unsw.relation.faculty Science
unsw.relation.originalPublicationAffiliation Ariyani, Ariyani, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Dooley, Anthony, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation an Huef, Astrid, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.school School of Mathematics & Statistics *
unsw.thesis.degreetype PhD Doctorate en_US
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