Geodesic
Pointwise Tur\'an 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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TIMM_2018_24_4_a12,
     author = {V. I. Ivanov},
     title = {Pointwise {Tur\'an} problem for periodic positive definite functions},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {156--175},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a12/}
}
TY  - JOUR
AU  - V. I. Ivanov
TI  - Pointwise Tur\'an problem for periodic positive definite functions
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2018
SP  - 156
EP  - 175
VL  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a12/
LA  - ru
ID  - TIMM_2018_24_4_a12
ER  - 
%0 Journal Article
%A V. I. Ivanov
%T Pointwise Tur\'an problem for periodic positive definite functions
%J Trudy Instituta matematiki i mehaniki
%D 2018
%P 156-175
%V 24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a12/
%G ru
%F TIMM_2018_24_4_a12
V. I. Ivanov. Pointwise Tur\'an 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/