Spherical Functions of Mathematical Geosciences: A Scalar, Vectorial, and Tensorial Setup

by Willi Freeden, Michael Schreiner

Overview

This book collects all material developed by the Geomathematics Group, TU Kaiserslautern, during the few last years to set up a theory of spherical functions of mathematical (geo-)physics. The work shows a twofold transition: First, the natural transition from the scalar to the vectorial and tensorial theory of spherical harmonics is given in coordinate-free representation, based on new variants of the addition theorem and the Funk-Hecke formulas. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is presented in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of constructive approximation and data analysis. In doing so, the whole palette of spherical (trial) functions is provided for modeling and simulating phenomena and processes of the Earth system.

Product Details

ISBN-13:	9783540851110
Publisher:	Springer Berlin Heidelberg
Publication date:	12/03/2008
Series:	Advances in Geophysical and Environmental Mechanics and Mathematics
Edition description:	2009
Pages:	602
Product dimensions:	6.50(w) x 9.50(h) x 1.70(d)

About the Author

Willi Freeden born in 1948 in Kaldenkirchen/Germany, Studies in Mathematics, Geography, and Philosophy at the RWTH Aachen, 1971 ‘Diplom’ in Mathematics, 1972 ‘Staatsexamen’ in Mathematics and Geography, 1975 PhD in Mathematics, 1979 ‘Habilitation’ in Mathematics, 1981/1982 Visiting Research Professor at the Ohio State University, Columbus (Department of Geodetic Sciences and Surveying), 1984 Professor of Mathematics at the RWTH Aachen (Institute of Pure and Applied Mathematics), 1989 Professor of Technomathematics, 1994 Head of the Geomathematics Group, 2002-2006 Vice-president for Research and Technology at the University of Kaiserslautern.

Michael Schreiner born in 1966 in Mertesheim/Germany, Studies in Industrial Mathematics, Mechanical Engineering, and Computer Science at the University of Kaiserslautern, 1991 ‘Diplom’ in Industrial Mathematics, 1994 PhD in Mathematics, 2004 ‘Habilitation’ in Mathematics. 1997–2001 researcher and project leader at the Hilti Corp. Schaan, Liechtenstein, 2002 Professor for Industrial Mathematics at the University of Buchs NTB, Buchs, Switzerland. 2004 Head of the Department of Mathematics of the University of Buchs, 2004 also Lecturer at the University of Kaiserslautern.

Table of Contents

Basic Settings and Spherical Nomenclature.- Scalar Spherical Harmonics.- Green’s Functions and Integral Formulas.- Vector Spherical Harmonics.- Tensor Spherical Harmonics.- Scalar Zonal Kernel Functions.- Vector Zonal Kernel Functions.- Tensorial Zonal Kernel Functions.- Zonal Function Modeling of Earth’s Mass Distribution.

Editorial Reviews

From the reviews:

"This book concentrates the introduction of mathematical representation of spherical vector and tensor fields. Vector/tensor spherical harmonics are used throughout mathematics. This book is a valuable reference for scientists and practitioners when facing spherical problems." (Chengshu Wang, Zentralblatt MATH, Vol. 1167, 2009)

From the Publisher