"This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. ..."
"Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classi ..."
"This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. ..."
"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 wo ..."
"In this chapter we consider analysis associated with symmetric groups. The
differential–difference operators for these groups, called type A in Weyl group
nomenclature, are crucial in this theory. The techniques tend to be algebraic,
relying on methods from combinatorics and linear algebra. Nevertheless the
chapter culminates in explicit evaluations of norm formulae and integrals of the
Macdonald–Mehta–Selberg type. These integrals ..."
Springer Monographs in Mathematics Approximation Theory and Harmonic Analysis on Spheres and Balls by Feng Dai, YuanXu 440 Pages, Published 2013 by Springer Science & Business Media ISBN-13: 978-1-4614-6660-4, ISBN: 1-4614-6660-1
"Feng Dai, Yuan Xu. Let J denote the integral in the above inequality. Then the
proof of (13.5.2) will follow once the following claim is established: for t > 3| K| +
d+ 1, "TZlKl J < c . 13.5.5 — 2/r(n;21)\/%(11;y)(1+"dir(21,y))H'"'IdIl ( ) First, from the
definition of z(x, y, t), we obtain the lower estimate 1—z(x,y,t) Z 1— 1/x1y1_ ---— 1
/Xd+1yd+1:1— cosdqp(x,y) d 2 I 2sin2 > EdT(r,y)2, (13.5.6) which enables us to
deduce the est ..."
Pitman Research Notes in Mathematics Ser. Common Zeros of Polynomials in Several Variables and Higher Dimensional Quadrature 312 by YuanXu Hardcover, Published 1994 by Longman Publishing Group ISBN-13: 978-0-470-23462-4, ISBN: 0-470-23462-8
Bamboo and Me Exploring Bamboo's Many Uses in Daily Life; A Story Told in English and Chinese by Xu Bin, Yuan Yahuan, Yijin Wert Hardcover, 42 Pages, Published 2018 by Shanghai Press ISBN-13: 978-1-60220-454-6, ISBN: 1-60220-454-3
Songs of the Immortals(1st Edition) An Anthology of Classical Chinese Poetry (Penguin Poetry) by XuYuan Zhong, Yuan-Chung Hsu Paperback, 256 Pages, Published 1994 by Puffin ISBN-13: 978-0-14-058685-5, ISBN: 0-14-058685-7