Admissible Wavelets Associated with the Affine Automorphism Group of the Siegel Upper Half-Plane
✍ Scribed by Jianxun He; Heping Liu
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 231 KB
- Volume
- 208
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
Let P s NAM be the minimal parabolic subgroup of SU n q 1, 1 , which can be regarded as the affine automorphism group of the Siegel upper half-plane U nq 1 , P also acts on the Heisenberg group H n , the boundary of U nq 1 . Therefore P has a 2 Ž n . 2 Ž n . natural representation U on L H . We decompose L H into the direct sum of the irreducible invariant closed subspaces under U. The restrictions of U on these subspaces are square-integrable. We give the characterization of the admissible condition in terms of the Fourier transform and define the wavelet transform with respect to admissible wavelets. The wavelet transform gives isometric operators 2 Ž n . 2 Ž .