On the expansion of a function in terms of spherical harmonics in arbitrary dimensions (Q1900896)

The paper is concerned in the expansion of a function, defined on a sphere of arbitrary dimension, in an uniformly convergent Laplace series of spherical harmonics -- as established by \textit{D. L. Ragozin} [Math. Ann. 195, 87-94 (1972; Zbl 0221.42018)] --, and in an uniformly absolutely convergent Laplace series, due to F. Rellich in his famous Göttingen lectures from 1952/53. The quotation and the refinement of these results is embedded in a careful and abundant survey of their history, moreover: this is not an itemizing of authors and papers related to this field, but the recent paper discusses -- e.g. -- the ideas, the construction, the ways, and the deficiencies of the relevant proofs found in the literature. Hence: a paper with a high level of mathematical culture.