Limits of functions on groups

Abstract

Our goal is to develop a limit approach for a class of problems in additive combinatorics that is analogous to the limit theory of dense graph sequences. We introduce a metric, convergence and limit objects for functions on discrete groups and use it to study limits of measurable functions on compact abelian groups. As an application we find exact minimizers for densities of linear configurations of complexity $1$.

Locations

• Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) - View - PDF
• Transactions of the American Mathematical Society - View