Lipschitz functions on the infinite-dimensional torus

Autor:	Bo'az Klartag, Dmitry Faifman
Rok vydání:	2014
Předmět:	Pure mathematics Computer Science::Information Retrieval Applied Mathematics General Mathematics Spectrum (functional analysis) Probability (math.PR) Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 020206 networking & telecommunications Torus Metric Geometry (math.MG) 0102 computer and information sciences 02 engineering and technology Function (mathematics) Lipschitz continuity 01 natural sciences Mathematics - Metric Geometry 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Computer Science::General Literature Mathematics::Symplectic Geometry Mathematics - Probability Mathematics
DOI:	10.48550/arxiv.1411.1620
Popis:	We discuss the spectrum phenomenon for Lipschitz functions on the infinite-dimensional torus. Suppose that [Formula: see text] is a measurable, real-valued, Lipschitz function on the torus [Formula: see text]. We prove that there exists a number [Formula: see text] with the following property: For any [Formula: see text], there exists a parallel, infinite-dimensional subtorus [Formula: see text] such that the restriction of the function [Formula: see text] to the subtorus [Formula: see text] has an [Formula: see text]-norm of at most [Formula: see text].
Databáze:	OpenAIRE
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