A. I. Aptekarev, A. Draux, D. N. Tulyakov, “On asymptotics of the sharp constants of the Markov–Bernshtein inequalities for the Sobolev spaces with coherent weights”, Keldysh Institute preprints, 2017,059, 20 pp.

On asymptotics of the sharp constants of the Markov–Bernshtein inequalities for the Sobolev spaces with coherent weights

A. I. Aptekarev^a, A. Draux^b, D. N. Tulyakov^a

^a Keldysh Institute of Applied Mathematics, Russian Academy of Science, Miusskaya Pl.4, Moscow 125047, Russian Federation
^b INSA de ROUEN, Avenue de l’Université -BP 8, 76801 Saint-Etienne-du-Rouvray Cedex FRANCE

Abstract: The Sobolev spaces with continuous and discrete coherent pairs of weights is considered. The positivity of the inner product is equivalent to the Markov–Bernstein inequality for the weighted integral norm. Asymptotics of the sharp constants for these inequalities when degree of polynomials goes to infinity are obtained.

Keywords: Markov–Bernstein inequalities; Sobolev orthogonal polynomials; continuous and discrete weights; coherent pairs; asymptotics of solutions of difference equations.

UDC: 517.53+517.9

Language: English

DOI: 10.20948/prepr-2017-59-e