2024/09/02 by Saúl Rodríguez Martín, Martín, Saúl Rodríguez
Computer Science · Engineering · Mathematics · #28D15 (Primary) #37A05 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory #Topological and Geometric Data Analysis #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2409.00885
openalex publication_date 2024/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain an inverse of Furstenberg's correspondence principle in the setting of countable cancellative, amenable semigroups. Besides being of intrinsic interest on its own, this result allows us to answer a variety of questions concerning sets of recurrence and van der Corput (vdC) sets, which were posed by Bergelson and Lesigne \citeBL, Bergelson and Ferré Moragues \citeBF, Kelly and Lê \citeKL, and Moreira \citeMor. We also prove a spectral characterization of vdC sets and prove some of their basic properties in the context of countable amenable groups. Several results in this article were independently found by Sohail Farhangi and Robin Tucker-Drob, see \citeFT.