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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2005, Volume 11, Number 2, Pages 92–111
(Mi timm192)
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This article is cited in 6 scientific papers (total in 6 papers)
Some extremal problems for periodic functions with conditions on their values and Fourier coefficients
V. I. Ivanov, D. V. Gorbachev, Yu. D. Rudomazina
Abstract:
A solution of the discrete variant of the Fejér problem on the greatest value, at zero, of an even nonnegative trigonometric polynomial with fixed average is given. As a corollary, for all rational $h$, $0<h\le1/2$, the
greatest averages are obtained for continuous 1-periodic even functions, with nonnegative Fourier coefficients
and a fixed value at zero, equal to zero on the segment $[h,1-h]$ (the Turán problem) or nonpositive on this
segment (the Delsarte problem). Similar problems are also solved in the discrete case. In addition, in one
case, a solution of the extremal Montgomery problem for nonnegative trigonometric polynomials is given.
Received: 10.09.2004
Citation:
V. I. Ivanov, D. V. Gorbachev, Yu. D. Rudomazina, “Some extremal problems for periodic functions with conditions on their values and Fourier coefficients”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 92–111; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S139–S159
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https://www.mathnet.ru/eng/timm192 https://www.mathnet.ru/eng/timm/v11/i2/p92
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Abstract page: | 612 | Full-text PDF : | 180 | References: | 61 |
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