3 papers
math.CT2026
A Categorical Framework for the Direct Integration of Banach Spaces
Daniel Funck, Giacomo Gavelli
We construct a categorical framework in which we can view the direct integral as a functor taking as input objects in a certain category of Abstract Banach bundles and outputting a…
math.SP2026
Spectral convergence of hyperbolic surfaces and quantum ergodicity
Giacomo Gavelli
We extend the notion of Plancherel convergence, introduced in the study of compact quotients of locally compact groups, to finite-area hyperbolic surfaces and establish a quantum e…
math.GR2024
Benjamini-Schramm vs Plancherel convergence
Giacomo Gavelli, Claudius Kamp
We show that Plancherel convergence is strictly stronger than Benjamini-Schramm convergence. In order to do so, we introduce two criteria for Plancherel and Benjamini-Schramm conve…