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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.
Produkteigenschaften
- Artikelnummer: 9783662656914
- Medium: Buch
- ISBN: 978-3-662-65691-4
- Verlag: Springer
- Erscheinungstermin: 15.10.2022
- Sprache(n): Englisch
- Auflage: 2. Auflage 2022
- Serie: Geosystems Mathematics
- Produktform: Gebunden
- Gewicht: 1273 g
- Seiten: 729
- Format (B x H x T): 160 x 241 x 46 mm
- Ausgabetyp: Kein, Unbekannt
- Vorauflage: 978-3-540-85111-0, 978-3-642-09881-9
Themen
- Naturwissenschaften
- Physik
- Physik Allgemein
- Theoretische Physik, Mathematische Physik, Computerphysik
- Naturwissenschaften
- Physik
- Physik Allgemein
- Theoretische Physik, Mathematische Physik, Computerphysik