Approximation Theory and Harmonic Analysis on Spheres and Balls

  • Feng Dai
  • Yuan Xu

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Feng Dai, Yuan Xu
    Pages 1-27
  3. Feng Dai, Yuan Xu
    Pages 79-103
  4. Feng Dai, Yuan Xu
    Pages 105-126
  5. Feng Dai, Yuan Xu
    Pages 127-153
  6. Feng Dai, Yuan Xu
    Pages 155-187
  7. Feng Dai, Yuan Xu
    Pages 213-239
  8. Feng Dai, Yuan Xu
    Pages 241-263
  9. Feng Dai, Yuan Xu
    Pages 265-296
  10. Feng Dai, Yuan Xu
    Pages 297-331
  11. Feng Dai, Yuan Xu
    Pages 333-361
  12. Feng Dai, Yuan Xu
    Pages 363-401
  13. Back Matter
    Pages 403-440

About this book

Introduction

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.

Keywords

Littlewood-Paley theory analysis on the sphere approximation theory harmonic analysis modulus of smoothness multiplier theorem spherical harmonics

Authors and affiliations

  • Feng Dai
    • 1
  • Yuan Xu
    • 2
  1. 1., Dept. Math. and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2., Department of MathematicsUniversity of OregonEugeneUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-6660-4
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-6659-8
  • Online ISBN 978-1-4614-6660-4
  • Series Print ISSN 1439-7382
  • About this book