Authors:
- Written by experts in the field
- Contains up-to-date research in approximation theory and harmonic analysis on balls and spheres
- Provides useful research material for both experts and advanced graduate students
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
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)Authors and Affiliations
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, Dept. Math. and Statistical Sciences, University of Alberta, Edmonton, Canada
Feng Dai
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, Department of Mathematics, University of Oregon, Eugene, USA
Yuan Xu
About the authors
Bibliographic Information
Book Title: Approximation Theory and Harmonic Analysis on Spheres and Balls
Authors: Feng Dai, Yuan Xu
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-6660-4
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-6659-8Published: 17 April 2013
Softcover ISBN: 978-1-4939-0131-9Published: 22 May 2015
eBook ISBN: 978-1-4614-6660-4Published: 17 April 2013
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XVIII, 440
Topics: Analysis, Approximations and Expansions, Fourier Analysis, Special Functions