×

Admissible wavelets and inverse Radon transform associated with the affine homogeneous Siegel domains of type. II. (English) Zbl 1134.42339

Summary: Let \(D(\Omega,\Phi)\) be the affine homogeneous Siegel domain of type II, whose Shilov 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 R. S. Strichartz [J. Funct. Anal. 96, No. 2, 350–406 (1991; Zbl 0734.43004)]. We devise a subspace of \(L^2(N)\) on which the Radon transform is a bijection. Using the wavelet inverse transform, we establish an inversion formula of the Radon transform in the weak sense.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
32A50 Harmonic analysis of several complex variables
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
43A85 Harmonic analysis on homogeneous spaces
65T60 Numerical methods for wavelets

Citations:

Zbl 0734.43004
PDFBibTeX XMLCite
Full Text: DOI