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

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