| |  Online-Ressource |
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| Verfasst von: | Freeden, Willi [VerfasserIn]  |
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| | Schreiner, Michael [VerfasserIn] |
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| Titel: | Spherical Functions of Mathematical Geosciences |
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| Titelzusatz: | A Scalar, Vectorial, and Tensorial Setup |
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| Verf.angabe: | by Willi Freeden, Michael Schreiner |
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| Ausgabe: | 2nd ed. 2022. |
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| Verlagsort: | Berlin, Heidelberg |
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| | Berlin, Heidelberg |
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| Verlag: | Springer Berlin Heidelberg |
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| | Imprint: Birkhäuser |
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| E-Jahr: | 2022 |
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| Jahr: | 2022. |
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| | 2022. |
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| Umfang: | 1 Online-Ressource(XV, 729 p. 74 illus., 71 illus. in color.) |
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| Gesamttitel/Reihe: | Geosystems Mathematics |
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| ISBN: | 978-3-662-65692-1 |
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| Abstract: | 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. |
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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. |
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| DOI: | doi:10.1007/978-3-662-65692-1 |
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| URL: | Resolving-System: https://doi.org/10.1007/978-3-662-65692-1 |
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| | DOI: https://doi.org/10.1007/978-3-662-65692-1 |
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| Schlagwörter: | (s)Geostatistik / (s)Dreidimensionales Modell / (s)Modellierung / (s)Kugelflächenfunktion |
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| | (s)Geowissenschaften / (s)Kugelfunktion |
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| Datenträger: | Online-Ressource |
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| Sprache: | eng |
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| Bibliogr. Hinweis: | Erscheint auch als : Druck-Ausgabe |
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| | Erscheint auch als : Druck-Ausgabe |
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| | Erscheint auch als : Druck-Ausgabe |
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| K10plus-PPN: | 1819109178 |
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| Lokale URL UB: |  Zum Volltext |
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Spherical Functions of Mathematical Geosciences / Freeden, Willi [VerfasserIn]; 2022. (Online-Ressource)
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