Geodesic
Concentration of the $L_1$-norm of trigonometric polynomials and entire functions
Sbornik. Mathematics, Tome 205 (2014) no. 11, pp. 1620-1649

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

For any sufficiently large $n$, the minimal measure of a subset of $[-\pi,\pi]$ on which some nonzero trigonometric polynomial of order $\le n$ gains half of the $L_1$-norm is shown to be $\pi/(n+1)$. A similar result for entire functions of exponential type is established. Bibliography: 13 titles.
Keywords: trigonometric polynomials, entire functions, extremal problems
Mots-clés : $L_1$-norm. 
@article{SM_2014_205_11_a3,
     author = {Yu. V. Malykhin and K. S. Ryutin},
     title = {Concentration of the $L_1$-norm of trigonometric polynomials and entire functions},
     journal = {Sbornik. Mathematics},
     pages = {1620--1649},
     publisher = {mathdoc},
     volume = {205},
     number = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_11_a3/}
}
TY  - JOUR
AU  - Yu. V. Malykhin
AU  - K. S. Ryutin
TI  - Concentration of the $L_1$-norm of trigonometric polynomials and entire functions
JO  - Sbornik. Mathematics
PY  - 2014
SP  - 1620
EP  - 1649
VL  - 205
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2014_205_11_a3/
LA  - en
ID  - SM_2014_205_11_a3
ER  - 
%0 Journal Article
%A Yu. V. Malykhin
%A K. S. Ryutin
%T Concentration of the $L_1$-norm of trigonometric polynomials and entire functions
%J Sbornik. Mathematics
%D 2014
%P 1620-1649
%V 205
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2014_205_11_a3/
%G en
%F SM_2014_205_11_a3
Yu. V. Malykhin; K. S. Ryutin. Concentration of the $L_1$-norm of trigonometric polynomials and entire functions. Sbornik. Mathematics, Tome 205 (2014) no. 11, pp. 1620-1649. http://geodesic.mathdoc.fr/item/SM_2014_205_11_a3/