Markov type polynomial inequality for some generalized Hermite weight

Year, pages: 2011, 111 - 118

In this paper we study some weighted polynomial inequalities of Markov type in $L^2$-norm. We use the properties of the system of generalized Hermite polynomials $\{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 $$ W(x)=|x|^{2\alpha } { e}^{- x^2},\qquad \alpha > -{1\over 2}. $$ The classical Hermite polynomials $H_n (x)$ present the special case for $\alpha =0$.

Ftorek, B., Marčoková, M. 2011. Markov type polynomial inequality for some generalized Hermite weight. In Tatra Mountains Mathematical Publications, vol. 49, no.2, pp. 111-118. 1210-3195.

Ftorek, B., Marčoková, M. (2011). Markov type polynomial inequality for some generalized Hermite weight. Tatra Mountains Mathematical Publications, 49(2), 111-118. 1210-3195.