Pointwise Fourier Inversion of Distributions on Projective Spaces

Abstract

Given a distribution $T$ on the real, complex or quaternionic projective space we define, in analogy to the work of Łojasiewicz, the value of $T$ at a point $z$ of the projective space and we show that, if $T$ has the value $\tau$ at $z$, then the Fourier-Laplace series of $T$ at $z$ is Abel-summable to $\tau$.