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Solutions to 6 problems in recurrence and Van der Corput sets
Sohail Farhangi, Saúl Rodríguez Martín
We present solutions to six problems concerning sets of nice recurrence and van der Corput (vdC) sets. We answer a question of Moreira, repeated by Fish and Skinner, by showing tha…
Multipliers and Disjointness from Mixing
Sohail Farhangi, Joel Moreira, Rigoberto Zelada
In 2005, Parreau proved that if a measure preserving system is not strongly mixing then it contains a non-trivial factor that is disjoint from every strongly mixing system. Taking…
The Theory of Normality for Dynamically Generated Cantor Series Expansions
Sohail Farhangi, Bill Mance
The theory of normality for base expansions of real numbers in is rich and well developed. Similar theories have been developed for many other numeration systems, such…
Asymptotic dynamics on amenable groups and van der Corput sets
Sohail Farhangi, Robin Tucker-Drob
We answer a question of Bergelson and Lesigne by showing that the notion of van der Corput set does not depend on the Følner sequence used to define it. This result has been discov…
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…
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…
Pointwise Ergodic Theorems for Higher Levels of Mixing
Sohail Farhangi
We prove strengthenings of the Birkhoff Ergodic Theorem for weakly mixing and strongly mixing measure preserving systems. We show that our pointwise theorem for weakly mixing syste…
A generalization of van der Corput's Difference Theorem
Sohail Farhangi
We prove a generalization of van der Corput's Difference Theorem in the theory of uniform distribution by establishing a connection with unitary operators that have Lebesgue spectr…