Harmonic Analysis of Analytic Functions on Hyperspheres

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....

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 1972-07, Vol.13 (7), p.950-955
Main Author: Beers, Brian Lee
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1666093