ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 31, 28 Symeonidis, Eleutherius, Katholische Universität Eichstätt, Germany The Poisson integral as an appropriate mean value We present a short, group-assisted proof of the following theorem of M. Vignati: The Poisson integral of a function f over a sphere S ⊆ ℝ^{n+1} at an interior point x coincides with the average of the Poisson integrals at x of f over all intersections of S with hyperplanes passing through x. The statement remains true, if the hyperplanes are replaced by affine kdimensional subspaces, for 1 ≤ k ≤ n. Reference: M. Vignati, On the factorization of Poisson integrals on spheres, preprint, Università degli Studi di Milano, 1990.