Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer Monographs in Mathematics), by Feng Dai, Yuan Xu
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Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer Monographs in Mathematics), by Feng Dai, Yuan Xu
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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. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography.
This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer Monographs in Mathematics), by Feng Dai, Yuan Xu- Published on: 2015-05-22
- Released on: 2015-05-22
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.04" w x 6.10" l, 1.41 pounds
- Binding: Paperback
- 440 pages
Review
From the reviews:
“This research monograph is recommended to graduate students, mathematicians, physicists, and engineers who have an interest in analysis and approximation on the sphere, ball, and simplex. … At the end of each chapter one finds useful ‘notes and further results’, where the authors present an account of the sources used for the developments in the chapter as well as comments on related results.” (P. P. Petrushev, Mathematical Reviews, January, 2014)
“The book under review is the most detailed monograph on harmonic analysis, approximation and their applications in the spherical setting. … This monograph in whole and its various parts can be used both by researchers and by lecturers, for information and ideas by the formers and as a matter for special courses for students by the latters.” (Elijah Liflyand, zbMATH, Vol. 1275, 2014)From the Back Cover
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. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography.
This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
About the Author Feng Dai is currently a professor of mathematics at the University of Alberta, and Yuan Xu is currently a professor of mathematics at the University of Oregon.
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Most helpful customer reviews
2 of 2 people found the following review helpful. Good book in approximation and harmonic analysis on spheres and balls By Yu Guang Wang This is a book of Feng Dai and Yuan Xu who are both experts in approximations on spheres and balls. It contains the recent (up to 2013) progress in approximation by localized kernel on the sphere and weighted approximation as well as the introduction to the quadrature rules on the sphere, where the latest proof by Bondarenko et al. of the existence of spherical design is included.
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