On Higher-Dimensional Oscillation in Ergodic Theory
Ben Krause
TL;DR
This paper extends existing results on higher-dimensional oscillation in ergodic theory by transferring the problem to the integer lattice and applying harmonic analysis techniques.
Contribution
It introduces new methods for analyzing higher-dimensional oscillation in ergodic theory through transference and harmonic analysis.
Findings
Extended results on oscillation in ergodic theory.
Applied harmonic analysis techniques to ergodic problems.
Generalized previous theorems to higher dimensions.
Abstract
We extend the results of Jones, Rosenblatt, and Wierdl concerning higher-dimensional oscillation in ergodic theory in a variety of ways. We do so by transference to the integer lattice, where we employ technique from (discrete) harmonic analysis.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Modeling in Engineering · advanced mathematical theories