Rapid decay for Fell bundles over étale groupoids gives analytic control and localizability in reduced cross-sectional C*-algebras, holds for polynomial-growth groupoids, equates to the group case for partial actions, but is blocked by exponential growth from branching in Deaconu-Renault groupoids.
[Tak14] Takuya Takeishi,On nuclearity ofC ∗-algebras of Fell bundles over ´ etale groupoids, Publ
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Rapid decay and localizability for Fell bundles over etale Groupoids
Rapid decay for Fell bundles over étale groupoids gives analytic control and localizability in reduced cross-sectional C*-algebras, holds for polynomial-growth groupoids, equates to the group case for partial actions, but is blocked by exponential growth from branching in Deaconu-Renault groupoids.