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.
| ISBN: | 9783662656914 |
| Publication date: | 15th October 2022 |
| Author: | Willi Freeden, Michael Schreiner |
| Publisher: | Springer-Verlag an imprint of Springer-Verlag Berlin and Heidelberg GmbH & Co. KG |
| Format: | Hardback |
| Pagination: | 729 pages |
| Series: | Geosystems Mathematics |
| Genres: |
Geology, geomorphology and the lithosphere Applied mathematics |