Correlations and Convergence Rates in General Ergodic Theorems

Key Points

• The research aims to explore the relationship between correlations and the convergence rates of ergodic averages in specific group actions.
• Develop mathematical formulas for calculating norms of deviations.
• Examine known correlations related to ergodic averages.
• Discuss illustrative examples to clarify findings.
• Investigate the inverse problem in recovering sums from norms.
• Formulas for norms of deviations were established using current correlations.
• Illustrative examples provided insights into the findings.
• Solutions for recovering sums from known norms were suggested.