Czechoslovak Mathematical Journal, online first, 12 pp.

Pointwise Fourier inversion of distributions on spheres

Francisco Javier González Vieli

Received July 27, 2016.   First published October 6, 2017.

Francisco Javier González Vieli, Montoie 45, 1007 Lausanne, Switzerland, e-mail: francisco-javier.gonzalez@gmx.ch

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

Classification (MSC 2010): 42C10, 46F12

DOI: 10.21136/CMJ.2017.0403-16

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