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.
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Böttcher, A., Dörfler, P. On the best constants in Markov-type inequalities involving Laguerre norms with different weights. Monatsh Math 161, 357–367 (2010). https://doi.org/10.1007/s00605-009-0187-y
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DOI: https://doi.org/10.1007/s00605-009-0187-y