Spherical Functions of Mathematical Geosciences

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The book offers a comprehensive overview of the theory of spherical functions, emphasizing a transition from scalar to vectorial and tensorial theories of spherical harmonics within a coordinate-free framework. It discusses key concepts such as the addition theorem, Funk-Hecke formulas, and Helmholtz decompositions. Additionally, it explores the shift from spherical harmonics to zonal functions and the Dirac kernel, linking these to an uncertainty principle relevant for data analysis in geosciences. The structured collection of spherical functions aims to aid in modeling Earth's system phenomena, making it significant for both research and education.