On some Rajchman measures and a solution to Salem's problem revisited
Abstract
We construct certain Rajchman measures by using integrability properties of the Fourier and Fourier-Stieltjes transforms. Further we show that Minkowski's question mark function ?(x), which is a singular monotone function, belongs to one of these classes. This circumstance leads us to a rigorous proof of the problem posed by R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943), p. 439) whether Fourier-Stieltjes coefficients of this function vanish at infinity and whose affirmative solution was recently announced by the author in [13]. Moreover, we generalize this problem, proving that derivatives of any order of the Fourier-Stieltjes transform with respect to the measure ?(x) tend to zero as well.
Keywords
Cite
@article{arxiv.1112.4605,
title = {On some Rajchman measures and a solution to Salem's problem revisited},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1112.4605},
year = {2011}
}
Comments
This paper has been withdrawn by the author due to a gap at the end of proof of Theorem 1