Springer Monographs in Mathematics

Approximation Theory and Harmonic Analysis on Spheres and Balls

Authors: Dai, Feng, Xu, Yuan

  • ​​​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
see more benefits

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-6660-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4614-6659-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4939-0131-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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.

About the authors

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.

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)

Table of contents (14 chapters)

  • Spherical Harmonics

    Dai, Feng (et al.)

    Pages 1-27

  • Convolution Operator and Spherical Harmonic Expansion

    Dai, Feng (et al.)

    Pages 29-51

  • Littlewood–Paley Theory and the Multiplier Theorem

    Dai, Feng (et al.)

    Pages 53-78

  • Approximation on the Sphere

    Dai, Feng (et al.)

    Pages 79-103

  • Weighted Polynomial Inequalities

    Dai, Feng (et al.)

    Pages 105-126

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-6660-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4614-6659-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4939-0131-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Approximation Theory and Harmonic Analysis on Spheres and Balls
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-6660-4
DOI
10.1007/978-1-4614-6660-4
Hardcover ISBN
978-1-4614-6659-8
Softcover ISBN
978-1-4939-0131-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVIII, 440
Topics