Spherical functions of mathematical geosciences : a scalar, vectorial, and tensorial setup / Willi Freeden, Michael Schreiner.
Freeden, W. (Willi), author.; Schreiner, M. (Michael), author.
2022
QE33.2.M3
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Title Spherical functions of mathematical geosciences : a scalar, vectorial, and tensorial setup / Willi Freeden, Michael Schreiner.
Author Freeden, W. (Willi), author.
Edition Second edition.
ISBN 9783662656921 (electronic bk.)
3662656922 (electronic bk.)
9783662656914
3662656914
DOI https://doi.org/10.1007/978-3-662-65692-1
Published Berlin, Germany : Birkhäuser, 2022.
Language English
Description 1 online resource : illustrations (black and white, and color).
Other Standard Identifiers 10.1007/978-3-662-65692-1 doi
Call Number QE33.2.M3
Dewey Decimal Classification 550.151553
Summary 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.
Note Previous edition: 2009.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Schreiner, M. (Michael), author.
Series Geosystems mathematics.
Available in Other Form Spherical functions of mathematical geosciences.
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
Basic Settings and Spherical Nomenclature
Scalar Spherical Harmonics
Greens 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 Earths Mass Distribution.

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