Nikol'skii Inequality Between the Uniform Norm and L-q-Norm with Ultraspherical Weight of Algebraic Polynomials on an Interval / Arestov Vitalii,Deikalova Marina // COMPUTATIONAL METHODS AND FUNCTION THEORY. - 2015. - V. 15, l. 4, SI. - P. 689-708.

ISSN/EISSN:

1617-9447 / 2195-3724

Type:

Article

Abstract:

We study the Nikol'skii inequality for algebraic polynomials on the interval {[}-1, 1] between the uniform norm and the norm of the space L-q(phi), 1 <= q < infinity, with the ultraspherical weight phi(x) = phi((alpha)) (x) = (1 - x(2))(alpha), alpha >= -1/2. We prove that the polynomial with unit leading coefficient that deviates least from zero in the space L-q(psi) with the Jacobi weight psi(x) = phi((alpha+1,alpha)) (x) = (1 - x)(alpha+1) (1 + x)(alpha) is an extremal polynomial in the Nikol'skii inequality. To prove this result, we use the generalized translation generated by the ultraspherical weight.

Author keywords:

Algebraic polynomial; Nikol'skii inequality; Polynomials that deviate least from zero; Generalized translation BROTHERS-TYPE INEQUALITY; TRIGONOMETRIC POLYNOMIALS; SPACES L; INTEGRAL-INEQUALITIES; CLOSED INTERVAL; DERIVATIVES; METRICS

DOI:

10.1007/s40315-015-0134-y

Web of Science ID:

ISI:000365748900012

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	DEC
Publisher	SPRINGER HEIDELBERG
Address	TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY
Language	English
EISSN	2195-3724
Keywords-Plus	BROTHERS-TYPE INEQUALITY; TRIGONOMETRIC POLYNOMIALS; SPACES L; INTEGRAL-INEQUALITIES; CLOSED INTERVAL; DERIVATIVES; METRICS
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	vitalii.arestov@urfu.ru marina.deikalova@urfu.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}15-01-02705]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (Project No. 15-01-02705) and by the Program for State Support of Leading Universities of the Russian Federation (Agreement No. 02.A03.21.0006 of August 27, 2013).
Number-of-Cited-References	42
Usage-Count-Since-2013	2
Journal-ISO	Comput. Methods Funct. Theory
Doc-Delivery-Number	CX5NN