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Abstract
Reciprocal integrals are constructed so that { H , h } constitutes a dual transform pair where H is a harmonic function in R 4 and h is the associated analytic function in C 3 . Necessary and sufficient conditions for the harmonic continuation to encounter singularities are linked to properties of the analytic continuation and conversely. Thus, Szego's theorem regarding zonal harmonic series and analytic functions in C 1 has a function theoretic extension to several variables.
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