The generalized continuous wavelet transform on Hilbert modules

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Copyright: Ariyani, Ariyani
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.
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Author(s)
Ariyani, Ariyani
Supervisor(s)
Dooley, Anthony
an Huef, Astrid
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Publication Year
2008
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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