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Monatshefte für Mathematik

, Volume 161, Issue 4, pp 357–367 | Cite as

On the best constants in Markov-type inequalities involving Laguerre norms with different weights

Article
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Abstract

The paper concerns best constants in Markov-type inequalities between the norm of a higher derivative of a polynomial and the norm of the polynomial itself. The norm of the polynomial is taken in L 2 on the half-line with the weight t α e −t and the derivative is measured in L 2 on the half-line with the weight t β e −t . Under an additional assumption on the difference β − α, we determine the leading term of the asymptotics of the constants as the degree of the polynomial goes to infinity.

Keywords

Markov inequality Laguerre polynomial Toeplitz matrix Volterra operator 

Mathematics Subject Classification (2000)

Primary 41A44 Secondary 15A18 26D10 45D05 47B35 
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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Fakultät für MathematikTU ChemnitzChemnitzGermany
  2. 2.Department Mathematik und InformationstechnologieMontanuniversität LeobenLeobenAustria

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