On $4$-lacunary sequences generated by ergodic toral endomorphisms
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- by Karol Krzyżewski PDF
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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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 469-478
- MSC: Primary 28D05
- DOI: https://doi.org/10.1090/S0002-9939-1993-1139478-3
- MathSciNet review: 1139478