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By Xu, Yuan
The purpose of this monograph is to study the common zeroes of families of polynomials in several variables which are related to higher dimensional quadrature. It aims to introduce a new approach and use it to conduct a systematic study.
Presents a systematic study of the common zeros of polynomials in several variables which are related to higher dimensional quadrature. The author uses a new approach which is based on the recent development of orthogonal polynomials in several variables and differs significantly... from the previous ones based on algebraic ideal theory. Featuring a great deal of new work, new theorems and, in many cases, new proofs, this self-contained work will be of great interest to researchers in numerical analysis, the theory of orthogonal polynomials and related subjects.Read more
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By Dai, Feng; Xu, Yuan
Presenting current results on analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes, this book covers distribution of points on the sphere, the reconstruction algorithm in computerized tomography and more.
By Dai, Feng; Xu, Yuan; Edited by Tikhonov, Sergey
a This book provides an introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The authors' focus is on the anal...ysis side of both h-harmonics and Dunkl transforms.Read more
By Dunkl, Charles F.; Xu, Yuan
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
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