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On 4-lacunary sequences generated by ergodic toral endomorphisms. (English) Zbl 0783.42016

Let \(\varphi\) be an ergodic endomorphism of the \(k\)-dimensional torus \(T^ k\) and \(f\) a sufficiently regular complex-valued function on \(T^ k\) with zero Haar integral. The author proves that then \((f\circ \varphi^ n)\), \(n\geq 1\), is a 4-lacunary sequence.
Applications are given to (i) the convergence of series, (ii) a generalization of the ergodic theorem, (iii) the existence of solutions of a generalized cohomology equation, and (iv) the convergence of moments in the central limit theorem.
Reviewer: F.Móricz (Szeged)

MSC:

42C15 General harmonic expansions, frames
28D05 Measure-preserving transformations
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