Jacobi Translation and the Inequality of Different Metrics for Algebraic Polynomials on an Interval / Arestov V. V.,Deikalova M. V. // DOKLADY MATHEMATICS. - 2017. - V. 95, l. 1. - P. 21-25.

ISSN/EISSN:

1064-5624 / 1531-8362

Type:

Article

Abstract:

The sharp inequality of different metrics (Nikol'skii's inequality) for algebraic polynomials in the interval {[}- 1, 1] between the uniform norm and the norm of the space L-q((alpha,beta)), l <= q <= infinity, with Jacobi weight,, is investigated. The study uses the generalized translation operator phi((alpha,beta))(x) = (1 - x )(alpha) (1 - x)(beta), alpha >= beta > -1, is investigates. the study uses the generalized translation operator generated by the Jacobi weight. A set of functions is described for which the norm of this operator in the space L-q((alpha,beta)), l <= q <= infinity, alpha >= beta > -1/2, is attained.

Author keywords:

NIKOLSKII INEQUALITY; UNIFORM NORM; SERIES; WEIGHT

DOI:

10.1134/S1064562417010100

Web of Science ID:

ISI:000399585800007

Соавторы в МНС:

Другие поля

Поле	Значение
Month	JAN
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8362
Keywords-Plus	NIKOLSKII INEQUALITY; UNIFORM NORM; SERIES; WEIGHT
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	vitalii.arestov@urfu.ru marina.deikalova@urfu.ru
Funding-Acknowledgement	program ``Leading Scientific Schools{''} {[}NSh-9356.2016.1]; Competitiveness Enhancement Program of Ural Federal University of the Government of the Russian Federation {[}211, 02.A03.21.0006]
Funding-Text	This work was supported by the program ``Leading Scientific Schools{''} (project no. NSh-9356.2016.1) and by the Competitiveness Enhancement Program of Ural Federal University (Enactment no. 211 of the Government of the Russian Federation of March 16, 2013, agreement no. 02.A03.21.0006 of August 27, 2013).
Number-of-Cited-References	15
Usage-Count-Last-180-days	2
Usage-Count-Since-2013	2
Journal-ISO	Dokl. Math.
Doc-Delivery-Number	ES5NA