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arXiv · 2412.05410

Fourier coefficients and rapid decay in reduced groupoid C*-algebras

Adam H. Fuller·Pradyut Karmakar
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Abstract

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 $G$.

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Adam H. Fuller, Pradyut Karmakar. 2024-12-06. Fourier coefficients and rapid decay in reduced groupoid C*-algebras. https://arxiv.org/abs/2412.05410

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