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math.DS2021★ 1 cited
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…
math.DS2021
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…