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Spherical functions of mathematical geosciencesa scalar, vectorial, and tensorial setup /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Spherical functions of mathematical geosciencesby Willi Freeden, Michael Schreiner.
其他題名:	a scalar, vectorial, and tensorial setup /
作者:	Freeden, W.
其他作者:	Schreiner, M.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg :2022.
面頁冊數:	xv, 729 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Earth sciencesMathematics.
電子資源:	https://doi.org/10.1007/978-3-662-65692-1
ISBN:	9783662656921$q(electronic bk.)

Spherical functions of mathematical geosciencesa 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$q(electronic bk.)

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

276480
Earth sciences
--Mathematics.

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

Dewey Class. No.: 550.151553

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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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