Harmonic Analysis on Internally Gelfand Pairs Associated to Groupoids
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 conv...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Etamaths Publishing
2019-11-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/1829 |
| Summary: | 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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| ISSN: | 2291-8639 |