Nilsequences, null-sequences, and multiple correlation sequences
نویسندگان
چکیده
منابع مشابه
Nilsequences, null-sequences, and multiple correlation sequences
A (d-parameter) basic nilsequence is a sequence of the form ψ(n) = f(ax), n ∈ Z, where x is a point of a compact nilmanifold X, a is a translation on X, and f ∈ C(X); a nilsequence is a uniform limit of basic nilsequences. If X = G/Γ be a compact nilmanifold, Y is a subnilmanifold of X, (g(n))n∈Zd is a polynomial sequence in G, and f ∈ C(X), we show that the sequence φ(n) = R g(n)Y f is the sum...
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In [MR], the second author and H. P. Rosenthal constructed the first examples of weakly null normalized sequences which do not have any unconditionally basic subsequences. Much more recently, the second author and W. T. Gowers [GM] constructed infinite dimensional Banach spaces which do not contain any unconditionally basic sequences. These later examples are of a different character than the e...
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Let (X;B; ; T ) be a measure preserving system, i.e. (X;B; ) is a probability space and T : X ! X a measurable and measure preserving map. We assume that the system is ergodic: T 1A = A ) (A) = 0 or (A) = 1. In order to investigate the way T "mixes" the space we can look at sequences of the form cn = (A \ T nB), for A;B 2 B. T is strongly mixing if cn ! (A) (B) and weakly mixing if the converge...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2013
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2013.36