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<p>Let <i>K</i> be a compact subgroup of a locally compact group <i>G</i>. We investigate a Pompeiu type problem for homogeneous spaces <i>G</i>/<i>K</i>. Suppose <i>E</i> is a compact subset of <i>G</i>/<i>K</i>. Using recent work of László Székelyhidi on <i>K</i>-spectral analysis [L. Székelyhidi, Spherical spectral synthesis. Acta Math. Hungar. 153(1), 120–142 (2017)] we are able to give necessary and sufficient conditions for <i>E</i> to have the Pompeiu property when (<i>G</i>,&#xa0;<i>K</i>) is a Gelfand pair.</p>

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The Pompeiu problem and spherical spectral analysis

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • Michael J. Puls

摘要

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 László Székelyhidi on K-spectral analysis [L. Székelyhidi, Spherical spectral synthesis. Acta Math. Hungar. 153(1), 120–142 (2017)] we are able to give necessary and sufficient conditions for E to have the Pompeiu property when (G, K) is a Gelfand pair.