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Spherical functions of mathematical geosciences : a scalar, vectorial, and tensorial setup / Willi Freeden, Michael Schreiner.

Second edition.

9783662656921 (electronic bk.)
3662656922 (electronic bk.)
9783662656914
3662656914

Berlin, Germany : Birkhäuser, 2022.

English

1 online resource : illustrations (black and white, and color).

10.1007/978-3-662-65692-1 doi

QE33.2.M3

550.151553

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.

Previous edition: 2009.

Includes bibliographical references and index.

Access limited to authorized users.

Description based on print version record.

Geosystems mathematics.

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