Quantitative convergence of weighted ergodic averages

Key Points

• This research aims to identify conditions under which weighted ergodic averages converge pointwise.
• Investigated conditions for sequences of weights to ensure convergence.
• Provided uniform decay rates in Fourier space for guaranteed convergence.
• Constructed a counterexample to explore boundary conditions.
• Established concrete uniform decay rates that lead to convergence.
• Demonstrated a counterexample illustrating conditions at the boundary.
• Suggested practical applications of the findings.