TY  - GEN
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.
DO  - 10.1007/978-3-662-65692-1
DO  - doi
AB  - 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.
T1  - Spherical functions of mathematical geosciences :a scalar, vectorial, and tensorial setup /
AU  - Freeden, W.
AU  - Schreiner, M.
ET  - Second edition.
CN  - QE33.2.M3
N1  - Previous edition: 2009.
ID  - 1450634
KW  - Earth sciences
KW  - Spherical functions.
SN  - 9783662656921
SN  - 3662656922
TI  - Spherical functions of mathematical geosciences :a scalar, vectorial, and tensorial setup /
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-662-65692-1
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-662-65692-1
ER  -