Yuan Xu
University of Oregon
314 Papers
2K Citations
Yuan Xu is an academic researcher from University of Oregon. The author has contributed to research in topics: Orthogonal polynomials & Unit sphere. The author has an hindex of 40, co-authored 302 publications. Previous affiliations of Yuan Xu include University of Southern Indiana & Temple University.
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Papers
Integration of the intertwining operator for $h$-harmonic polynomials associated to reflection groups
Yuan Xu
- 01 Jan 1997
TL;DR: In this article, it was shown that the expansion of a continuous function as Fourier series in h-harmonics with respect to hαdω is uniformly Cesáro (C, δ) summable on the sphere if δ > |α|1 + (d− 2)/2, provided that the intertwining operator is positive.
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Sub-exponentially localized kernels and frames induced by orthogonal expansions
TL;DR: In this article, the authors construct supexponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, spherical harmonics, orthogonality on the ball and simplex, and Hermite and Laguerre functions.
A characterization of positive quadrature formulae
TL;DR: In this article, it was shown that the quasi-orthogonal polynomials that lead to the positive quadrature formulae can all be expressed as characteristic polynoms of a symmetric tridiagonal matrix with positive subdiagonal entries.
Orthogonal Structure on a Wedge and on the Boundary of a Square
Sheehan Olver,Yuan Xu +1 more
TL;DR: A basis of Orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier orthogonal expansions is studied, and the basis is used to calculate Stieltjes transforms.
Approximation by Means of h -Harmonic Polynomials on the Unit Sphere
TL;DR: A weighted modulus of smoothness is defined using the modified spherical means and is proved to be equivalent to a weighted K-modulusdefined using the differential-difference h-spherical Laplacian.