Böttcher, Albrecht ; Dörfler, Peter : Inequalities of the Markov type for partial derivatives of polynomials in several variables

Author(s):

Böttcher, Albrecht
Dörfler, Peter

Title:

Inequalities of the Markov type for partial derivatives of polynomials in several variables

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 7, 2009

Mathematics Subject Classification:

41A10			[ Approximation by polynomials ]
15A18			[ Eigenvalues, singular values, and eigenvectors ]
26D10			[ Inequalities involving derivatives and differential and integral operators ]
35P15			[ Estimation of eigenvalues, upper and lower bounds ]
41A63			[ Multidimensional problems ]
45D05			[ Volterra integral equations ]

Abstract:

First order asymptotic formulas for the best constants in inequalities of the Markov type with L^2 norms for partial derivatives of polynomials in several variables are derived. The principal coefficient in the leading term of the formulas is identifed as the operator norm of a Volterra integral operator and is studied in detail.

Keywords:

Markov inequality, orthogonal polynomials, Volterra integral operators, partial differential operator, polynomials of several variables

Language:

English

Publication time:

4 / 2009