TY  - BOOK
AU  - Freeden,Willi
AU  - Schreiner,Michael
TI  - Spherical Functions of Mathematical Geosciences: A Scalar, Vectorial, and Tensorial Setup 
T2  - Geosystems Mathematics,
SN  - 9783662656921
PY  - 2022///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Birkhäuser
KW  - Mathematics
KW  - Solid Earth Sciences
KW  - Applications of Mathematics
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-662-65692-1
ER  -