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Van der Corput sets in $ℤ^{d}$

100%

Bergelson V., Lesigne E.

Colloquium Mathematicum

2008

tom 110

nr 1

1-49

In this partly expository paper we study van der Corput sets in $ℤ^{d}$, with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some classical results obtained for d = 1 by Kamae and M. Mendès France and by Ruzsa, establish new characterizations, introduce and discuss some modifications of van der Corput sets which correspond to various notions of recurrence, provide numerous examples and formulate some natural open questions.

Large deviations for generic stationary processes

100%

Lesigne E., Volný D.

Colloquium Mathematicum

2000

tom 84/85

nr 1

75-82

Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Lesigne E.

1 Bergelson V.

1 Volný D.

1 2008

1 2000

Wyniki wyszukiwania

Van der Corput sets in $ℤ^{d}$

Large deviations for generic stationary processes