Divergent Square Averages
Zoltan Buczolich (Eotvos Lorand University, Budapest, Hungary), R., Daniel Mauldin (University of North Texas, Denton, TX)
TL;DR
This paper demonstrates that the sequence of square numbers does not satisfy L^1-universal convergence, answering a question posed by Bourgain and highlighting limitations in ergodic averages.
Contribution
It proves that the sequence n^2 is L^1-universally bad, providing a significant counterexample in ergodic theory.
Findings
Sequence n^2 is L^1-universally bad.
Answers Bourgain's question on divergence.
Highlights limitations of square averages in ergodic theory.
Abstract
We answer a question of J. Bourgain. We show that the sequence n^2 is L^1-universally bad.
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Mathematics and Applications