MARKOV TYPE POLYNOMIAL INEQUALITY FOR SOME GENERALIZED HERMITE WEIGHT
Ftorek, Branislav ; Marčoková, Mariana
Tatra Mountains Mathematical Publications, Tome 49 (2011), / Harvested from Mathematical Institute
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 In this paper we study some weighted polynomial inequalities of Markov type in $L^2$-norm.We use the properties ofthe system of generalized Hermitepolynomials $\{H^{(\alpha)} _n (x)\}_{n=0}^{\infty} $. The polynomials$H^{(\alpha)} _n (x) $ are orthogonal in$\mathbb{R}=(-\infty,\infty )$ with respect to the weight function $$W(x)=|x|^{2\alpha } { e}^{- x^2},\ \ \alpha > -{1\over 2}. $$The classical Hermite polynomials $H_n (x)$ present the special casefor $\alpha =0$.

Publié le : 2011-01-01
DOI : https://doi.org/10.2478/tatra.v49i0.126 
@article{126,
     title = {MARKOV TYPE POLYNOMIAL INEQUALITY FOR SOME GENERALIZED HERMITE WEIGHT},
     journal = {Tatra Mountains Mathematical Publications},
     volume = {49},
     year = {2011},
     doi = {10.2478/tatra.v49i0.126},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/126}
}

Ftorek, Branislav; Marčoková, Mariana. MARKOV TYPE POLYNOMIAL INEQUALITY FOR SOME GENERALIZED HERMITE WEIGHT. Tatra Mountains Mathematical Publications, Tome 49 (2011) . doi : 10.2478/tatra.v49i0.126. http://gdmltest.u-ga.fr/item/126/