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math.GR2023
Koopman representations for positive definite functions
Sohail Farhangi
We show that for any locally compact second countable group and any continuous positive definite function , there exists an ergodic measure preserving…
math.DS2023
Van der Corput's difference theorem for amenable groups and the left regular representation
Sohail Farhangi
We establish a connection between two variants of van der Corput's Difference Theorem (vdCDT) for countably infinite amenable groups and the ergodic hierarchy of mixing propert…
math.DS2023★ 2 cited
A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages
Sohail Farhangi
We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between s…