Fourier coefficients and rapid decay in reduced groupoid C*-algebras
| Autor: | Fuller, Adam H., Karmakar, Pradyut |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\Sigma \rightarrow G$ be a twist over a locally compact Hausdorff \'{e}tale groupoid $G$. Given $f$ in the reduced C$^*$-algebra $C_r^*(\Sigma;G)$ with open support $U \subseteq G$ we ask when $f$ lies in the closure of the compactly supported sections on $U$. Suppose $G$ satisfies the rapid decay property with respect to a length function $L$. We give a positive answer to our question in two instances: when $L$ is conditionally negative-definite, and when $L$ is the square-root of a locally negative type function on $G$. Comment: 15 pages |
| Databáze: | arXiv |
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