On some Rajchman measures and equivalent Salem's problem

2011/12/28 by Semyon Yakubovich, Yakubovich, Semyon
Mathematics · #Functional Equations Stability Results #Fuzzy Systems and Optimization #math.CA #msc:33C10 #msc:42A16 #msc:42B10 #msc:44A15

paper · pdf · doi:10.48550/arxiv.1112.6147

Salem's problem is still open. This article is about an equivalent problem, which possibly can contribute to a final solution

arxiv created 2011/12/28 · arxiv updated 2011/12/30

Abstract

We construct certain Rajchman measures by using integrability properties of the Fourier and Fourier-Stieltjes transforms. In particular, we state a problem and prove that it is equivalent to the known and still unsolved question posed by R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943), p. 439) whether Fourier-Stieltjes coefficients of the Minkowski's question mark function vanish at infinity.

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