IP-rigidity and eigenvalue groups

Abstract

We examine the class of increasing sequences of natural numbers which are IP-rigidity sequences for some weakly mixing probability preserving transformation. This property is closely related to the uncountability of the eigenvalue group of a corresponding non-singular transformation. We give examples, including a super-lacunary sequence which is not IP-rigid.

Some converses added

References in corpus (1)

• Rigidity and Non-recurrence along Sequences

Cited by in corpus (2)

• Conditions for rational weak mixing
• Good sequences with uncountable spectrum and singular asymptotic distribution