Existence of large independent-like sets
Tom 159 / 2020
Streszczenie
Let be a compact abelian group and \varGamma be its discrete dual group. For N \in \mathbb N , we define a class of independent-like sets, N-PR sets, to be sets in \Gamma such that every \mathbb Z _N-valued function defined on the set can be interpolated by a character in G.
These sets are examples of \varepsilon -Kronecker sets and Sidon sets. In this paper we study various properties of N-PR sets. We give a characterization of N-PR sets, describe their structure and prove the existence of large N-PR sets.