Czechoslovak Mathematical Journal, first online, pp. 1-12
Pointwise Fourier inversion of distributions on spheres
Francisco Javier González Vieli
Received July 27, 2016. First published October 6, 2017
Abstract: Given a distribution $T$ on the sphere we define, in analogy to the work of Łojasiewicz, the value of $T$ at a point $\xi$ of the sphere and we show that if $T$ has the value $\tau$ at $\xi$, then the Fourier-Laplace series of $T$ at $\xi$ is Abel-summable to $\tau$.
Keywords: distribution; sphere; Fourier-Laplace series; Abel summability