Geometric properties of the Lebesgue function

Abstract

We present a collection of observations concerning the peculiar behavior of the Lebesgue function in the setting of the interval $[-1,1]\subset \mathbb{R}$ and the square $[-1,1{]}^2\subset {\mathbb{R}}^2$. We provide numerical results and formulate several open problems related to the geometry of the Lebesgue function.

13 pages, 24 figures