On Nikol'skii type inequality between the uniform norm and the integral q-norm with Laguerre weight of algebraic polynomials on the half-line / Arestov Vitalii,Deikalova Marina,Horvath Agota // JOURNAL OF APPROXIMATION THEORY. - 2017. - V. 222, l. . - P. 40-54.

ISSN/EISSN:

0021-9045 / 1096-0430

Type:

Article

Abstract:

We study the Nikol'skii type inequality for algebraic polynomials on the half-line {[}0,infinity] between the ``uniform{''} norm sup\{|f(x)|e(-x/2) : x is an element of {[}0,infinity] and the norm (integral(infinity)(0)|f(x)e(-x/2)|(q)x(alpha)dx)(1/q) of the space L-alpha(q) with the Laguerre weight for 1 <= q < and alpha >= 0. It is proved that the polynomial with a fixed leading coefficient that deviates least from zero in the space L-alpha+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 L-alpha(q) are studied. (C) 2017 Elsevier Inc. All rights reserved.

Author keywords:

Algebraic polynomial; Nikol'skii inequality; Laguerre weight; Laguerre translation INTERVAL

DOI:

10.1016/j.jat.2017.05.005

Web of Science ID:

ISI:000411776700003

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	OCT
Publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE
Address	525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Language	English
EISSN	1096-0430
Keywords-Plus	INTERVAL
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	vitalii.arestov@urfu.ru marina.deikalova@urfu.ru ahorvath@math.bme.hu
Funding-Acknowledgement	Russian Foundation for Basic Research {[}15-01-02705]; Program for State Support of Leading Scientific Schools of Russian Federation {[}NSh-9356.2016.1]; Competitiveness Enhancement Program of Ural Federal University (Enactment of the Government of the Russian Federation) {[}211, 02.A03.21.0006]
Funding-Text	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).
Number-of-Cited-References	19
Journal-ISO	J. Approx. Theory
Doc-Delivery-Number	FI2NX