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On the expansion of a function in terms of spherical harmonics in arbitrary dimensions. (English) Zbl 0835.33006

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 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.

MSC:

33C55 Spherical harmonics
41-02 Research exposition (monographs, survey articles) pertaining to approximations and expansions
01A60 History of mathematics in the 20th century
01A55 History of mathematics in the 19th century

Citations:

Zbl 0221.42018
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