This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth’s system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.
Willi Freeden & Michael Schreiner
Spherical Functions of Mathematical Geosciences
A Scalar, Vectorial, and Tensorial Setup
Spherical Functions of Mathematical Geosciences
A Scalar, Vectorial, and Tensorial Setup
Dil İngilizce ● Biçim PDF ● Sayfalar 729 ● ISBN 9783662656921 ● Dosya boyutu 11.6 MB ● Yayımcı Springer Berlin Heidelberg ● Kent Heidelberg ● Ülke DE ● Yayınlanan 2022 ● Baskı 2 ● İndirilebilir 24 aylar ● Döviz EUR ● Kimlik 8659543 ● Kopya koruma Sosyal DRM