Abstract

As we have seen in the geomathematical motivation of Chap. 1, spherical functions are an essential tool for all geosciences. In this chapter we develop orthonormal function systems for scalar functions on spheres in the three-dimensional Euclidean space, namely the scalar spherical harmonics, which are then generalized to vectorial functions in Chap. 5 as well as to systems for scalar functions on spheres in the more general, q-dimensional setting in Chap. 6.

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