Lipschitz functions on the infinite-dimensional torus

2014/11/06 by Faifman, Dmitry, Klartag, Bo'az
#FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1411.1620

Abstract

We discuss the spectrum phenomenon for Lipschitz functions on the infinite-dimensional torus. Suppose that f is a measurable, real-valued, Lipschitz function on the torus \mathbbT^∞. We prove that there exists a number a ∈ \mathbb R with the following property: For any ε> 0 there exists a parallel, infinite-dimensional subtorus M ⊆ \mathbb T^∞ such that the restriction of the function f-a to the subtorus M has an L^∞(M)-norm of at most ε.

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