On some Rajchman measures and equivalent Salem's problem

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.

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

Cited by in corpus (1)

• Minkowski's question mark measure is UST--regular