English

On some Rajchman measures and equivalent Salem's problem

Classical Analysis and ODEs 2011-12-30 v1

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.

Cite

@article{arxiv.1112.6147,
  title  = {On some Rajchman measures and equivalent Salem's problem},
  author = {Semyon Yakubovich},
  journal= {arXiv preprint arXiv:1112.6147},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T19:57:43.173Z