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Matematicheskie Zametki, 2018, Volume 103, Issue 4, Pages 576–581
DOI: https://doi.org/10.4213/mzm11843 (Mi mzm11843) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$

K. A. Oganesyan

Lomonosov Moscow State University
Full-text PDF (398 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm11843
Abstract: Nonzero sine series with monotone coefficients tending to zero are considered. It is shown that the measure of the set of those zeros of such a series which belong to $[0,\pi]$ cannot exceed $\pi/3$. Moreover, if this value is attained, then almost all zeros belong to the closed interval $[2\pi/3,\pi]$.
Keywords: sine series, monotone coefficients, zeros of a function, measure of a set.
Received: 30.10.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 4, Pages 621–625
DOI: https://doi.org/10.1134/S000143461803029X
Bibliographic databases:
Document Type: Article
UDC: 517.518.45
Language: Russian
Citation: K. A. Oganesyan, “The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$”, Mat. Zametki, 103:4 (2018), 576–581; Math. Notes, 103:4 (2018), 621–625
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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