Admissible wavelets and inverse radon transform associated with the affine homogeneous Siegel domains of type II

作者：He, Jianxun^*; Liu, Heping

来源：Communications in Analysis and Geometry, 2007, 15(1): 1-28.

• INTEGRABLE GROUP-REPRESENTATIONS
• HARMONIC-ANALYSIS
• HEISENBERG-GROUP
• SPACES

Let D(Omega, Phi) be the affine homogeneous Siegel domain of type II, whose Silov boundary N is a nilpotent Lie group of step two. In this article, we develop the theory of wavelet analysis on N. By selecting a set of mutual orthogonal wavelets we give a direct sum decomposition of L-2(D(Omega, Phi)), the first component A(0,0)(0) of which is the Bergman space. Moreover, we study the Radon transform on N, and obtain an inversion formula R-1 = (pi)(-2d) LRL which is an extension of that by Strichartz [R. S. Strichartz, LP harmonic analysis and Radon transforms on the Heisenberg group, J. Funct. Anal. 96 (1991), 350-406.]. We devise a subspace of L-2(N) on which the Radon transform is a bijection. Using wavelet inverse transform, we establish an inversion formula of the Radon transform in the weak sense.

• 出版日期2007-1
• 单位北京大学; 广州大学