Markov type polynomial inequality for some generalized Hermite weight

Ftorek, Branislav; Marˇcokov´A, Mariana

doi:10.2478/v10127-011-0030-4

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 H_n(x) present the special case for α = 0.

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Markov type polynomial inequality for some generalized Hermite weight

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