PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Interpolation sets and nilsequences

Volume 162 / 2020

Anh N. Le Colloquium Mathematicum 162 (2020), 181-199 MSC: Primary 37A45; Secondary 11B30. DOI: 10.4064/cm7937-9-2019 Published online: 27 April 2020


To answer a question of Frantzikinakis, we study a class of subsets of $\mathbb {N}$, called interpolation sets, on which every bounded sequence can be extended to an almost periodic sequence on $\mathbb {N}$. It has been proved by Strzelecki that lacunary sets are interpolation sets. We prove that sets that are denser than all lacunary sets cannot be interpolation sets. We also extend the notion of interpolation sets to nilsequences and show that the analogue to Frantzikinakis’s question for arbitrary sequences has a negative answer.


  • Anh N. LeDepartment of Mathematics
    Northwestern University
    2033 Sheridan Road
    Evanston, IL 60208-2730, U.S.A.

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image