Admissibie wavelets on the unit disk ^∗

^∗ The work for this paper was supported by the National Science Foundation of China.

Abstract

Let .SU(1. 1) be the Mobius group, and K the maximal compact SU(1. 1). Then SU(1.1)/K can be regarded as the unit disk of complex plane In this paper, the unit disk is regarded as a homogeneous space, in the viewpoint of coherent state we give the admissible condition of admissible wavelet and the orthogonal decomposition of L^α,2(D,dμ_α).

Keywords:

• Admissible condition
• homogeneous space
• wavelet transform
• coherent state
• orthogonal decomposition
• reproducing kernel

Classification Categories::

• 1991 AMS Classification: 22D10
• 33C45
• 43A85
• 81R30

^∗ The work for this paper was supported by the National Science Foundation of China.

^∗ The work for this paper was supported by the National Science Foundation of China.

Notes

^∗ The work for this paper was supported by the National Science Foundation of China.