Czechoslovak Mathematical Journal, Vol. 67, No. 4, pp. 1059-1070, 2017


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
Classification MSC:  42C10, 46F12
DOI:  10.21136/CMJ.2017.0403-16

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

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