An estimate for coeffcients of polynomials in L2 norm, ii
Publications de l'Institut Mathématique, _N_S_58 (1995) no. 72, p. 137
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Let ${\Cal P}_n$ be the class of algebraic polynomials
$P(x)=\sum_{k=0}^na_kx^k$ of degree at most $n$ and $\|P\|_{d\sigma}=
(\int_R|P(x)|^2d\sigma(x))^{1/2}$, where $d\sigma(x)$ is a nonnegative
measure on $R$. We determine the best constant in the inequality
$|a_k|\le C_{n,k} (d\sigma)\|P\|_{d\sigma}$, for $k=0,1,\dots,n$, when
$P\in {\Cal P}_n$ and such that $P(\xi_k)=0$, $k=1,\dots,m$. The cases
$C_{n,n}(d\sigma)$ and $C_{n,n-1}(d\sigma)$ were studed by Milovanović
and Guessab [6]. In particular, we consider the case when the
measure $d\sigma(x)$ corresponds to generalized Laguerre orthogonal
polynomials on the real line.
@article{PIM_1995_N_S_58_72_a14,
author = {G.V. Milovanovi\'c and L.Z. Ran\v{c}i\'c},
title = {An estimate for coeffcients of polynomials in {L\protect\textsuperscript{2}} norm, ii},
journal = {Publications de l'Institut Math\'ematique},
pages = {137 },
publisher = {mathdoc},
volume = {_N_S_58},
number = {72},
year = {1995},
zbl = {0863.26012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1995_N_S_58_72_a14/}
}
TY - JOUR AU - G.V. Milovanović AU - L.Z. Rančić TI - An estimate for coeffcients of polynomials in L2 norm, ii JO - Publications de l'Institut Mathématique PY - 1995 SP - 137 VL - _N_S_58 IS - 72 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/PIM_1995_N_S_58_72_a14/ LA - en ID - PIM_1995_N_S_58_72_a14 ER -
G.V. Milovanović; L.Z. Rančić. An estimate for coeffcients of polynomials in L2 norm, ii. Publications de l'Institut Mathématique, _N_S_58 (1995) no. 72, p. 137 . http://geodesic.mathdoc.fr/item/PIM_1995_N_S_58_72_a14/