Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

  • Kendall Atkinson
  • Weimin Han

Part of the Lecture Notes in Mathematics book series (LNM, volume 2044)

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (volume 2044)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Kendall Atkinson, Weimin Han
    Pages 1-9
  3. Kendall Atkinson, Weimin Han
    Pages 11-86
  4. Kendall Atkinson, Weimin Han
    Pages 87-130
  5. Kendall Atkinson, Weimin Han
    Pages 131-163
  6. Kendall Atkinson, Weimin Han
    Pages 165-210
  7. Kendall Atkinson, Weimin Han
    Pages 211-236
  8. Back Matter
    Pages 237-244

About this book

Introduction

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as
an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.

Keywords

41A30, 65N30, 65R20 approximation theory quadrature spherical harmonic

Authors and affiliations

  • Kendall Atkinson
    • 1
  • Weimin Han
    • 2
  1. 1.Department of Mathematics &, Department of Computer ScienceUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsUniversity of Iowa CityIowa CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-25983-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-25982-1
  • Online ISBN 978-3-642-25983-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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