<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we study some weighted polynomial inequalities of Markov type in L2-norm. We use the properties of the system of generalized Hermite polynomials <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/v10127-011-0030-4#0008_graphic1.png"></inline-graphic></inline-formula>. The polynomials H(α)n (x) are orthogonal in ℝ = (−∞,∞) with respect to the weight function <disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/v10127-011-0030-4#0008_graphic2.png"></inline-graphic></disp-formula>.The classical Hermite polynomials Hn(x) present the special case for α = 0.</abstract>

In this paper we study some weighted polynomial inequalities of Markov type in L2-norm. We use the properties of the system of generalized Hermite polynomials . The polynomials H(α)n (x) are orthogonal in ℝ = (−∞,∞) with respect to the weight function .The classical Hermite polynomials Hn(x) present the special case for α = 0.

Markov type polynomial inequality for some generalized Hermite weight

Department of Applied Mathematics Faculty of Mechanical Engineering University of ˇZilina Univerzitn´a 1 SK–010-26 ˇZilina SLOVAKIA

Department of Mathematics Faculty of Science University of ˇZilina Univerzitn´a 1 SK–010-26 ˇZilina SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"Markov type polynomial inequality for some generalized Hermite weight"}

In this paper we study some weighted polynomial inequalities of Markov type in L2-norm. We use the properties of the system of generalized Hermite polynomials...

Markov type polynomial inequality for some generalized Hermite weight

Publié en ligne: 13 nov. 2012

Pages: 111 - 118

DOI: https://doi.org/10.2478/v10127-011-0030-4

Mots clés
Markov type inequality, weight function, generalized Hermite polynomials.

This content is open access.

Markov type polynomial inequality for some generalized Hermite weight

Publié en ligne: 13 nov. 2012

Pages: 111 - 118

DOI: https://doi.org/10.2478/v10127-011-0030-4

Mots clésMarkov type inequality, weight function, generalized Hermite polynomials.

This content is open access.

Mots clés
Markov type inequality, weight function, generalized Hermite polynomials.