Inversion Formulas for the Spherical Radon-Dunkl Transform

Zhongkai Li

Type: Article

Publication Date: 2009-03-03

Citations: 3

DOI: https://doi.org/10.3842/sigma.2009.025

Abstract

The spherical Radon-Dunkl transform R κ , associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of h-harmonics.Several inversion formulas of R κ are given with the aid of spherical Riesz-Dunkl potentials, the Dunkl operators, and some appropriate wavelet transforms.

Locations

Symmetry Integrability and Geometry Methods and Applications - View - PDF
The scientific electronic library of periodicals of the National Academy of Sciences of Ukraine (National Academy of Sciences of Ukraine) - View - PDF

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Works Cited by This (29)

Action	Title	Year	Authors
+ PDF Chat	Centrally symmetric convex bodies and the spherical Radon transform	1992	Paul Goodey Wolfgang Weil
+ PDF Chat	Integration of the intertwining operator for $h$-harmonic polynomials associated to reflection groups	1997	Yuan Xu
+	Fractional Integrals and Potentials	1996	Boris Rubin
+	A positive radial product formula for the Dunkl kernel	2003	Margit Rösler
+ PDF Chat	Weighted Approximation of Functions on the Unit Sphere	2003	Yuan Xu
+ PDF Chat	Intertwining Operator and <i>h</i>-Harmonics Associated With Reflection Groups	1998	Yuan Xu
+ PDF Chat	Spherical harmonics and integral geometry on projective spaces	1983	Eric L. Grinberg
+ PDF Chat	Integral Kernels with Reflection Group Invariance	1991	Charles F. Dunkl
+ PDF Chat	Almost Everywhere Convergence of Orthogonal Expansions of Several Variables	2004	Yuan Xu
+	Inversion of Fractional Integrals Related to the Spherical Radon Transform	1998	Boris Rubin