On the affirmative solution to Salem's problem

2014/12/31 by Semyon Yakubovich, Yakubovich, Semyon
Mathematics · #42A16 #42B10 #44A15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1501.00141

openalex publication_date 2014/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The Salem problem to verify whether Fourier-Stieltjes coefficients of the Minkowski question mark function vanish at infinity is solved recently affirmatively. In this paper by using methods of classical analysis and special functions we solve a Salem-type problem about the behavior at infinity of a linear combination of the Fourier-Stieltjes transforms. Moreover, as a consequence of the Salem problem, some asymptotic relations at infinity for the Fourier-Stieltjes coefficients of a power m∈ ℕ of the Minkowski question mark function are derived.

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