# Enhancements of van der Corput's Difference Theorem and Connections to the Hierarchy of Mixing Properties of Unitary Operators

@article{Farhangi2021EnhancementsOV, title={Enhancements of van der Corput's Difference Theorem and Connections to the Hierarchy of Mixing Properties of Unitary Operators}, author={Sohail Farhangi}, journal={arXiv: Dynamical Systems}, year={2021} }

We introduce some new variants of van der Corput's Difference Theorem in Hilbert spaces and juxtapose them with variants from the previous literature. We show that three of the variants from the previous literature correspond to weak mixing, strong mixing, and orthogonal bases in a Hilbert space (in a sense that will be made precise), and we introduce new variants corresponding to ergodicity and mild mixing. We correspondingly obtain 4 new variants of van der Corput's Difference Theorem in the…

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