Krzyżewski, Karol On 4-lacunary sequences generated by ergodic toral endomorphisms. (English) Zbl 0783.42016 Proc. Am. Math. Soc. 118, No. 2, 469-478 (1993). 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 Keywords:ergodic endomorphism; Haar integral; 4-lacunary sequence; convergence of series; ergodic theorem; cohomology equation; convergence of moments; central limit theorem PDFBibTeX XMLCite \textit{K. Krzyżewski}, Proc. Am. Math. Soc. 118, No. 2, 469--478 (1993; Zbl 0783.42016) Full Text: DOI