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Title
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The generalized continuous wavelet transform on Hilbert modules
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| Author(s) |
Ariyani, Mathematics & Statistics, Faculty of Science, UNSW
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| Resource Type |
Thesis
PhD Doctorate
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| Supervisor(s) |
Dooley, Anthony, Mathematics & Statistics, Faculty of Science, UNSW
an Huef, Astrid, Mathematics & Statistics, Faculty of Science, UNSW
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| Keyword(s) |
Continuous wavelet transform
Hilbert C*-Module
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| Date |
2008 |
| 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. |
| Language |
EN |
| Rights |
Please click here to view the rights |
| Print Availability |
T/2008/260 (Ask at Level 2 Information Desk, UNSW Library) |
| Citation Link |
Please use this identifier to cite or link to this item: http://handle.unsw.edu.au/1959.4/42151 |
| Full Text | 
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| Total Attachment(s) | 2 |
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