Admissible wavelets associated with the affine automorphism group of the Siegel upper half-plane

[摘要] Let P = NAM be the minimal parabolic subgroup of SU(n + 1, 1), which can be regarded as the affine automorphism group of the Siegel upper half-plane Un+1, P also acts on the Heisenberg group H-n, the boundary of Un+1. Therefore P has a natural representation U on L(2)(H-n). We decompose L(2)(H-n) 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 from the irreducible invariant closed subspaces of L(2)(H-n) to L(2)(P). (C) 1997 Academic Press.

[发布日期] 1997-04-01