Harmonic Analysis of Analytic Functions on Hyperspheres

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Abstract
The real analytic functions on the hypersphere Sn are shown to be in one-to-one correspondence with the family of series of hyperspherical harmonics with exponentially falling coefficients. These functions may be continued onto a larger complex manifold on which they represent holomorphic functions. The convergence of the harmonic expansions for the real analytic functions on Sn is governed by the singularity structure of the continued function on this complex manifold.

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