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Analysis of Spherical Symmetries in Euclidean Spaces : APPLIED MATHEMATICAL SCIENCES - Claus Muller

Analysis of Spherical Symmetries in Euclidean Spaces

APPLIED MATHEMATICAL SCIENCES

Hardcover

Published: 20th November 1997
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This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. Based on many years of lecturing to mathematicians, physicists and engineers in scientific research institutions in Europe and the USA, the author uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. One of the highlights is the extension of the classical results of the spherical harmonics into the complex - particularly important for the complexification of the Funk-Hecke formula which successfully leads to new integrals for Bessel- and Hankel functions with many applications of Fourier integrals and Radon transforms. Numerous exercises stimulate mathematical ingenuity and bridge the gap between well-known elementary results and their appearance in the new formations.

Preface
Introduction
Notations and Basic Theorems
The General Theory
Primitive Spaces
The Completeness
The Funk-Hecke Formula
Representations and Interpolations
Homogeneous Harmonics
The Specific Theories
The Legendre Polynomials
The Laplace Integrals
The Gegenbauer Polynomials
The Associated Legendre Functions
The Associated Spaces yj/n(q)
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387949499
ISBN-10: 0387949496
Series: APPLIED MATHEMATICAL SCIENCES
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 226
Published: 20th November 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.77 x 16.51  x 1.91
Weight (kg): 0.48