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Preprints of the Keldysh Institute of Applied Mathematics, 2017, 059, 20 pp.
DOI: https://doi.org/10.20948/prepr-2017-59-e (Mi ipmp2275) 		 
On asymptotics of the sharp constants of the Markov–Bernshtein inequalities for the Sobolev spaces with coherent weights

A. I. Aptekareva, A. Drauxb, D. N. Tulyakova

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
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DOI: https://doi.org/10.20948/prepr-2017-59-e
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.
Funding agency Grant number
Russian Science Foundation 14-21-00025
Document Type: Preprint
UDC: 517.53+517.9
Language: English
Citation: 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.
Citation in format AMSBIB
\Bibitem{AptDraTul17}
\by A.~I.~Aptekarev, A.~Draux, D.~N.~Tulyakov
\paper On asymptotics of the sharp constants of the Markov--Bernshtein inequalities for the Sobolev spaces with coherent weights
\jour Keldysh Institute preprints
\yr 2017
\papernumber 059
\totalpages 20
\mathnet{http://mi.mathnet.ru/ipmp2275}
\crossref{https://doi.org/10.20948/prepr-2017-59-e}
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    		Препринты Института прикладной математики им. М. В. Келдыша РАН
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