Absolute and Unconditional Convergence of Series of Ergodic Averages and Lebesgue Derivatives

TL;DR

This paper investigates conditions under which series of stochastic processes, including ergodic averages and Lebesgue derivatives, converge absolutely or unconditionally, bridging ergodic theory and harmonic analysis.

Contribution

It provides new criteria for absolute and unconditional convergence of series involving ergodic and harmonic analysis processes.

Findings

Established conditions for absolute convergence of ergodic averages.

Derived criteria for unconditional convergence in harmonic analysis.

Connected convergence properties across ergodic theory and harmonic analysis.

Abstract

We consider when there is absolute or unconditional convergence of series of various types of stochastic processes. These processes include differences of averages in ergodic theory and harmonic analysis, like the classical Cesaro average in ergodic theory and Lebesgue derivatives in harmonic analysis.