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
