caa a22 4500 605525676 CHVBK 20210128100759.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2483-5 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2483-5 Belov A. Ivanovo State University, Ivanovo, Russia aut On the Asymptotic Solution of One Extremal Problem Related to Nonnegative Trigonometric Polynomials [Elektronische Daten] [A. Belov] For every real number γ ≥ 1 we denote by K ↓(γ) the least possible value of the constant term of an even nonnegative trigonometric polynomial with monotone coefficients such that all its coefficients, save for the constant term, are not lesser than 1 and the sum of these coefficients equals γ. In this paper, the asymptotic estimate of K ↓(γ) is found and some extremal problems on the minimum of the constant term of an even nonnegative trigonometric polynomial are studied. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 19-50 1072-3374 209:1<19 2015 209 10958 https://doi.org/10.1007/s10958-015-2483-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2483-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Belov A. Ivanovo State University, Ivanovo, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 19-50 1072-3374 209:1<19 2015 209 10958