Harmonic Analysis on Internally Gelfand Pairs Associated to Groupoids

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Let G be a topological locally compact, Hausdorff and second countable groupoid with a Haar system and K a proper subgroupoid of G with a Haar system too. (G, K) is an internally Gelfand pair if for any u in the unit space, the algebra of bi-K(u)-invariant functions on G(u) is commutative under convolution. In this work, we give some characterizations of these pairs and extend to this context some classical results of harmonic analysis.

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