We prove that a point x in R is out of the support of a pseudomeasure T on R if and only if the Fourier integral of T at x is summable with Cesàro means of order 1 to zero.

A finite measure supported by the unit sphere S n−1 in R n and absolutely continuous with respect to the natural measure on S n−1 is entirely determined by the restriction of its Fourier transform to a sphere of radius r if and only 2πr is not a zero of any Bessel function J d+(n−2)/2 with d a nonnegative integer.2010 Mathematics subject classification: primary 42B10; secondary 46F12.

We show that, given m, n two relatively prime natural numbers, if a complex valued function f on a homogeneous tree satisfies the mean value property for all spheres of radius m and all spheres of radius n, then f is harmonic.

B(x,R) f (z) dz. Si f est continue, la fonction x → B(x,R) f (z) dz est continûment dérivable par rapportà la l e variable ([Vo], II, p. 150). D'après (2) c'est donc

Inversion de Fourier ponctuelle des distributions a Á support compact Par FRANCISCO JAVIER GONZA  LEZ VIELI Re  sume Â. On montre que linte  grale de Fourier dune distribution a Á support compact est sommable en moyenne de Cesa Á ro uniforme  ment vers ze  ro au voisinage dun point si et seulement si ce point nappartient pas au support de la distribution. Archiv der MathematikMathematics Subject Classification (1991): Primary 46F12; Secondary 42B08.Travail re  alise  gra à ce a Á une bourse du Fonds national suisse de la recherche scientifique.