Limit theorems for lacunary weighted Cesaro methods

Elif N. Yildirim, Fatih Nuray

Abstract


In this paper, we study the asymptotic behavior of lacunary weighted Cesaro means. Building upon classical results in Cesaro summability, we extend the theory to the lacunary setting and establish sufficient conditions for the convergence of such means. The analysis includes both one-dimensional and multi-dimensional sequences, with applications to ergodic-type limits and central limit behavior. Several counterexamples are presented to illustrate the necessity of the assumptions and to highlight differences between classical and lacunary Cesaro methods.

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