On a problem by R. Salem concerning Minkowski's question mark function

2015/01/05 by Tomas Persson, Persson, Tomas
Mathematics · #42A16 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.DS #math.NT #msc:42A16

paper · pdf · doi:10.48550/arxiv.1501.00876

2 pages

arxiv created 2015/01/05 · arxiv updated 2015/01/07

Abstract

Minkowski's question mark function is strictly increasing on [0, 1] and hence defines a Stieltjes measure on [0, 1]. A problem originating from Salem in 1943, is to determine whether the Fourier series of this measure decay to zero or not. The purpose of this note is to mention that a recent result by Jordan and Sahlsten implies that the Fourier transform decays to zero with a polynomial speed.

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