IP-rigidity and eigenvalue groups
Jon. Aaronson, Maryam Hosseini, Mariusz Lemanczyk
TL;DR
This paper explores the properties of IP-rigidity sequences in weakly mixing transformations and their connection to eigenvalue groups, providing examples and counterexamples including a super-lacunary sequence.
Contribution
It introduces new insights into IP-rigidity sequences and their relation to eigenvalue groups, including the construction of a super-lacunary sequence that is not IP-rigid.
Findings
IP-rigidity sequences are closely related to the uncountability of eigenvalue groups.
Examples of IP-rigidity sequences are provided, including a super-lacunary sequence.
A super-lacunary sequence that is not IP-rigid is constructed.
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.
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