Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

2012
ISBN: 978-3-642-25982-1
Verlag: Springer

Buch, Englisch, Band 2044, 244 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 394 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Han, Weimin

Atkinson, Kendall

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

1 Preliminaries.- 2 Spherical Harmonics.- 3 Differentiation and Integration over the Sphere.- 4 Approximation Theory.- 5 Numerical Quadrature.- 6 Applications: Spectral Methods.