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arXiv · 2505.03048

The Pompeiu problem and spherical spectral analysis

Michael J. Puls
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Abstract

Let $K$ be a compact subgroup of a locally compact group $G$. We investigate a Pompeiu type problem for homogeneous spaces $G/K$. Suppose $E$ is a compact subset of $G/K$. Using recent work of L\'{a}szl\'{o} Sz\'{e}kelyhidi on $K$-spectral analysis \cite{Szekelyhidi17} we are able to give necessary and sufficient conditions for $E$ to have the Pompeiu property when $(G, K)$ is a Gelfand pair.

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Michael J. Puls. 2025-05-05. The Pompeiu problem and spherical spectral analysis. https://arxiv.org/abs/2505.03048

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