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Spherical Functions of Mathematical Geosciences = A Scalar, Vectorial, and Tensorial Setup /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Spherical Functions of Mathematical Geosciences/ by Willi Freeden, Michael Schreiner.
其他題名:	A Scalar, Vectorial, and Tensorial Setup /
作者:	Freeden, Willi.
其他作者:	Schreiner, Michael.
面頁冊數:	XV, 729 p. 74 illus., 71 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Applications of Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-662-65692-1
ISBN:	9783662656921

Spherical Functions of Mathematical Geosciences = A Scalar, Vectorial, and Tensorial Setup /
Freeden, Willi.

Spherical Functions of Mathematical GeosciencesA Scalar, Vectorial, and Tensorial Setup /[electronic resource] :by Willi Freeden, Michael Schreiner. - 2nd ed. 2022. - XV, 729 p. 74 illus., 71 illus. in color.online resource. - 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:

669175
Applications of Mathematics.

Spherical Functions of Mathematical Geosciences = A Scalar, Vectorial, and Tensorial Setup /
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