Keywords:
Mathematics.
;
Solid Earth Sciences.
;
Applications of Mathematics.
Description / 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.
Abstract:
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.
Type of Medium:
Online Resource
Pages:
XV, 729 p. 74 illus., 71 illus. in color.
,
online resource.
Edition:
2nd ed. 2022.
ISBN:
9783662656921
Series Statement:
Geosystems Mathematics,
URL:
https://doi.org/10.1007/978-3-662-65692-1
DOI:
10.1007/978-3-662-65692-1
Language:
English
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