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Spherical functions of mathematical ...

Freeden, W.

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Spherical functions of mathematical geosciences = a scalar, vectorial, and tensorial setup /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spherical functions of mathematical geosciences/ by Willi Freeden, Michael Schreiner.
Reminder of title:	a scalar, vectorial, and tensorial setup /
Author:	Freeden, W.
other author:	Schreiner, M.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2022.,
Description:	xv, 729 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Earth sciences - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-662-65692-1
ISBN:	9783662656921

Spherical functions of mathematical geosciences = a scalar, vectorial, and tensorial setup /
Freeden, W.

Spherical functions of mathematical geosciencesa scalar, vectorial, and tensorial setup /[electronic resource] :by Willi Freeden, Michael Schreiner. - Second edition. - Berlin, Heidelberg :Springer Berlin Heidelberg :2022. - xv, 729 p. :ill., digital ;24 cm. - Geosystems mathematics,2510-1552. - Geosystems mathematics..

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.

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: 9783662656921

Standard No.: 10.1007/978-3-662-65692-1doiSubjects--Topical Terms:

551200
Earth sciences
--Mathematics.

LC Class. No.: QE33.2.M3 / F74 2022

Dewey Class. No.: 550.151553

Spherical functions of mathematical geosciences = a scalar, vectorial, and tensorial setup /
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245 1 0 $a Spherical functions of mathematical geosciences $h [electronic resource] : $b a scalar, vectorial, and tensorial setup / $c by Willi Freeden, Michael Schreiner.
250 $a Second edition.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Birkhäuser, $c 2022.
300 $a xv, 729 p. : $b ill., digital ; $c 24 cm.
490 1 $a Geosystems mathematics, $x 2510-1552
505 0 $a 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.
520 $a 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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650 0 $a Spherical functions. $3 731269
650 1 4 $a Solid Earth Sciences. $3 3591737
650 2 4 $a Applications of Mathematics. $3 890893
700 1 $a Schreiner, M. $3 3607347
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856 4 0 $u https://doi.org/10.1007/978-3-662-65692-1
950 $a Earth and Environmental Science (SpringerNature-11646)