Spherical Functions of Mathematical Geosciences: A Scalar, Vectorial, and Tensorial Setup; Second Edition
Willi Freeden, Michael Schreiner
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.
年:
2022
版:
2
出版社:
Birkhäuser / Springer Berlin Heidelberg / Springer, Berlin
言語:
english
ページ:
730
ISBN 10:
3662656914
ISBN 13:
9783662656914
ファイル:
PDF, 10.76 MB
IPFS:
,
english, 2022
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