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On $ 4$-lacunary sequences generated by ergodic toral endomorphisms

Author: Karol Krzyżewski
Journal: Proc. Amer. Math. Soc. 118 (1993), 469-478
MSC: Primary 28D05
MathSciNet review: 1139478
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Abstract: It is proved that if $ \varphi $ is an ergodic endomorphism of $ {\mathbb{T}^k}$ and $ f$ is a sufficiently regular complex-valued function on $ {\mathbb{T}^k}$ with the Haar integral zero, then $ (f \circ {\varphi ^n})$ is a $ 4$-lacunary sequence. Within the class of ergodic toral endomorphisms and sufficiently regular complex-valued functions, applications are given to the convergence of series, a generalization of the ergodic theorem, the existence of solutions of a generalized cohomology equation, and the convergence of moments in the central limit theorem.

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