Geodesic
Pointwise Turán problem for periodic positive definite functions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 156-175
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We study the pointwise Turán problem on the largest value at an arbitrary point $x$ of a $1$-periodic positive definite function supported on the interval $[-h, h]$ and equal to $1$ at zero. For rational values of $x$ and $h$, the problem reduces to a discrete version of the Fejér problem on the largest value of the $\nu$th coefficient of an even trigonometric polynomial of order $p-1$ that has zero coefficient 1 and is nonnegative on a uniform grid $k/q$, $k=0,\dots,q-1$. The discrete Fejér problem is solved for a number of values of the parameters $\nu$, $p$, and $q$. In all the cases, we construct extremal polynomials and quadrature formulas, which yield an estimate for the largest coefficient.
Mots-clés : Fourier transform and series, quadrature formula
Keywords: periodic positive definite function, pointwise Turán problem, extremal polynomial. 
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V. I. Ivanov. Pointwise Turán problem for periodic positive definite functions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 156-175. http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a12/

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