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Weighted Markov-type inequalities, norms of Volterra operators, and zeros of Bessel functions

✍ Scribed by Albrecht Böttcher; Peter Dörfler

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
198 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The first term of the asymptotics of the best constants in Markov‐type inequalities for higher derivatives of polynomials is determined in the two cases where the underlying norm is the L^2^ norm with Laguerre weight or the L^2^ norm with Gegenbauer weight. The coefficient in this term is shown to be the norm of a certain Volterra integral operator which depends on the weight and the order of the derivative. For first order derivatives, the norms of the Volterra operators are expressed in terms of the zeros of Bessel functions. The asymptotic behavior of the coefficients is studied and tight bounds for them are given (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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