Analysis of Spherical Symmetries in Euclidean Spaces

Download or read book Analysis of Spherical Symmetries in Euclidean Spaces written by Claus Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.