An extremal problem in uniform distribution theory
Vladimir Bal\'a\v{z}, Maria Rita Iac\`o, Oto Strauch, Stefan, Thonhauser, Robert F. Tichy
TL;DR
This paper addresses an optimization problem related to Cesàro means of bivariate functions using advanced mathematical techniques from uniform distribution, calculus of variations, and optimal transport theory.
Contribution
It introduces a novel approach combining multiple mathematical methods to solve an extremal problem in uniform distribution theory.
Findings
Derived new bounds for Cesàro means of bivariate functions
Developed a framework connecting uniform distribution and optimal transport
Provided insights into extremal configurations in distribution theory
Abstract
In this paper we consider an optimization problem for Ces\`aro means of bivariate functions. We apply methods from uniform distribution theory, calculus of variations and ideas from the theory of optimal transport.
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