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Mathematics > Classical Analysis and ODEs

arXiv:1501.00141 (math)
[Submitted on 31 Dec 2014 (v1), last revised 19 May 2019 (this version, v11)]

Title:On the affirmative solution to Salem's problem

Authors:Semyon Yakubovich
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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 $m\in \mathbb{N}$ of the Minkowski question mark function are derived.
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 42A16, 42B10, 44A15
Cite as: arXiv:1501.00141 [math.CA]
  (or arXiv:1501.00141v11 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.1501.00141

Submission history

From: Semyon Yakubovich [view email]
[v1] Wed, 31 Dec 2014 14:22:40 UTC (9 KB)
[v2] Wed, 15 Apr 2015 12:44:36 UTC (10 KB)
[v3] Thu, 14 May 2015 15:45:37 UTC (10 KB)
[v4] Sun, 24 May 2015 15:27:58 UTC (10 KB)
[v5] Tue, 16 Jun 2015 12:53:46 UTC (10 KB)
[v6] Tue, 1 Dec 2015 10:11:51 UTC (10 KB)
[v7] Wed, 27 Apr 2016 12:51:37 UTC (14 KB)
[v8] Fri, 16 Dec 2016 13:19:04 UTC (12 KB)
[v9] Thu, 27 Sep 2018 09:40:22 UTC (12 KB)
[v10] Tue, 30 Oct 2018 14:11:46 UTC (12 KB)
[v11] Sun, 19 May 2019 07:54:20 UTC (12 KB)
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