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Quantifying Democracy of Wavelet Bases in Lorentz Spaces

The Solution of a Problem of Coifman, Meyer, and Wickerhauser on Wavelet Packets

Wavelets Techniques for Pointwise Anti-Hölderian Irregularity

Polyharmonic Approximation on the Sphere

A Generalized Radon Transform on the Plane

Approximation of Functions of Few Variables in High Dimensions

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A Generalized Radon Transform on the Plane

Content Provider	Springer Nature Link
Author	Song, Futao Li, Zhongkai
Copyright Year	2010
Abstract	A new generalized Radon transform R α, β on the plane for functions even in each variable is defined which has natural connections with the bivariate Hankel transform, the generalized biaxially symmetric potential operator Δα, β, and the Jacobi polynomials $P_{k}^{(\beta,\,\alpha)}(t)$ . The transform R α, β and its dual $R_{\alpha,\,\beta}^{\ast}$ are studied in a systematic way, and in particular, the generalized Fuglede formula and some inversion formulas for R α, β for functions in $L_{\alpha,\,\beta}^{p}(\mathbb{R}^{2}_{+})$ are obtained in terms of the bivariate Hankel–Riesz potential. Moreover, the transform R α, β is used to represent the solutions of the partial differential equations $Lu:=\sum_{j=1}^{m}a_{j}\Delta_{\alpha,\,\beta}^{j}u=f$ with constant coefficients a j and the Cauchy problem for the generalized wave equation associated with the operator Δα, β. Another application is that, by an invariant property of R α, β, a new product formula for the Jacobi polynomials of the type $P_{k}^{(\beta,\,\alpha)}(s)C_{2k}^{\alpha+\beta+1}(t)=c\int\!\!\int P_{k}^{(\beta,\,\alpha)}$ is obtained.
Ending Page	123
Page Count	31
Starting Page	93
File Format	PDF
ISSN	01764276
e-ISSN	14320940
Journal	Constructive Approximation
Issue Number	1
Volume Number	33
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-05-12
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Inversion formula Hankel transform Inverse problems Orthogonal functions and polynomials, general theory Analysis Numerical Analysis Jacobi polynomial Radon transform Generalized Radon transform Riesz potential
Content Type	Text
Resource Type	Article
Subject	Analysis Computational Mathematics

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On generalized Christoffel functions

Analysis Related to All Admissible Type Parameters in the Jacobi Setting

A generalized inversion formula for the continuous Jacobi transform

The Smallest Eigenvalue of Hankel Matrices

Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials

Harmonic analysis operators related to symmetrized Jacobi expansions

Generalized christoffel functions for Jacobi-exponential weights on [-1,1]

On Hankel Positive Definite Perturbations of Hankel Positive Definite Sequences and Interrelations to Orthogonal Matrix Polynomials

A Generalized Radon Transform on the Plane

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