Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111936
Title: On Nikol'skii Type Inequality between the Uniform Norm and the Integral q-norm with Laguerre Weight of Algebraic Polynomials on the Half-Line
Authors: Arestov, V.
Deikalova, M.
Horváth, Á.
Issue Date: 2017
Publisher: Academic Press Inc.
Elsevier BV
Citation: Arestov V. On Nikol'skii Type Inequality between the Uniform Norm and the Integral q-norm with Laguerre Weight of Algebraic Polynomials on the Half-Line / V. Arestov, M. Deikalova, Á. Horváth // Journal of Approximation Theory. — 2017. — Vol. 222. — P. 40-54.
Abstract: We study the Nikol'skii type inequality for algebraic polynomials on the half-line [0,∞) between the “uniform” norm sup{|f(x)|e−x∕2:x∈[0,∞)} and the norm ∫0 ∞|f(x)e−x∕2|qxαdx1∕q of the space Lα q with the Laguerre weight for 1≤q<∞ and α≥0. It is proved that the polynomial with a fixed leading coefficient that deviates least from zero in the space Lα+1 q is the unique extremal polynomial in the Nikol'skii inequality. To prove this result, we use the Laguerre translation. The properties of the norm of the Laguerre translation in the spaces Lα q are studied. © 2017 Elsevier Inc.
Keywords: ALGEBRAIC POLYNOMIAL
LAGUERRE TRANSLATION
LAGUERRE WEIGHT
NIKOL'SKII INEQUALITY
URI: http://hdl.handle.net/10995/111936
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85033360457
PURE ID: 2125858
ISSN: 0021-9045
metadata.dc.description.sponsorship: This work was supported by the Russian Foundation for Basic Research (Project No. 15-01-02705), by the Program for State Support of Leading Scientific Schools of the Russian Federation (Project no. NSh-9356.2016.1), and by the Competitiveness Enhancement Program of the Ural Federal University (Enactment of the Government of the Russian Federation of March 16, 2013 No. 211, Agreement No. 02.A03.21.0006 of August 27, 2013).
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