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 {m\in\mathbb{N}} of the Minkowski question mark function are derived.

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论塞勒姆问题的正解

摘要 验证闵可夫斯基问号函数的傅里叶-斯蒂尔杰斯系数是否在无穷远为零的塞勒姆问题最近得到了肯定的解决。在本文中，通过使用经典分析和特殊函数的方法，我们解决了关于傅里叶 - 斯蒂尔杰斯变换的线性组合在无穷远处的行为的塞勒姆型问题。此外，作为塞勒姆问题的结果，导出了闵可夫斯基问号函数的幂 m ∈ ℕ {m \ in \ mathbb {N}} 的傅立叶-斯蒂尔杰斯系数在无穷远的一些渐近关系。