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7 results on '"Song, Futao"'

1. Inversion Formulas for the Spherical Radon-Dunkl Transform

Author

Li, Zhongkai and Song, Futao

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Functional Analysis
Abstract

The spherical Radon-Dunkl transform $R_\kappa$, 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 $R_\kappa$ are given with the aid of spherical Riesz-Dunkl potentials, the Dunkl operators, and some appropriate wavelet transforms.

Published
2009
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3. Inversion of Riesz Potentials for Dunkl Transform.

Author

Liu, Moyi, Song, Futao, and Wang, Rongxin

Subjects
*RIESZ spaces, *WAVELET transforms, *AUTOMORPHISMS, *FOURIER transforms, *INVARIANT measures
Abstract

The inversion of Riesz potentials for Dunkl transform when G=Z2d is given by using the generalized wavelet transforms. It is also proved that the Riesz potentials Iακ are automorphisms on the Semyanistyi-Lizorkin spaces. [ABSTRACT FROM AUTHOR]

Published
2018
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7. Characterizations of Smoothness of Functions in Terms of their Jacobi Expansions.

Author

Li, Zhongkai, Song, Futao, and Li, Kai

Abstract

The smoothness of functions defined on (−1, 1) is characterized by the Poisson integrals of their Jacobi expansions. The generalized translation T and the generalized difference $${\widetilde{T}_t}$$ associated with the product formulas of Jacobi polynomials are used to illustrate the smoothness of functions, which leads to very natural generalizations of the classical results of Hardy-Littlewoood and Zygmund. [ABSTRACT FROM AUTHOR]

Published
2011
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