Trigonometric polynomials of least deviation from zero in measure and related problems / Arestov Vitalii V.,Mendelev Alexei S. // JOURNAL OF APPROXIMATION THEORY. - 2010. - V. 162, l. 10, SI. - P. 1852-1878.

ISSN/EISSN:

0021-9045 / нет данных

Type:

Article

Abstract:

We give a solution of the problem on trigonometric polynomials f(n) with the given leading harmonic y cos nt that deviate the least from zero in measure, more precisely, with respect to the functional mu(f(n)) = mes\{t is an element of {[}0, 2 pi] : vertical bar f(n)(t)vertical bar >= 1\}. For trigonometric polynomials with a fixed leading harmonic, we consider the least uniform deviation from zero on a compact set and find the minimal value of the deviation over compact subsets of the torus that have a given measure. We give a solution of a similar problem on the unit circle for algebraic polynomials with zeros on the circle. (C) 2010 Elsevier Inc. All rights reserved.

Author keywords:

Trigonometric polynomials of least deviation from zero; Deviation in measure; Uniform norm on compact sets CHEBYSHEV POLYNOMIALS

DOI:

10.1016/j.jat.2010.07.007

Web of Science ID:

ISI:000283564600006

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
Keywords-Plus	CHEBYSHEV POLYNOMIALS
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	Vitalii.Arestov@usu.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}08-01-00213]; Russian Federation {[}NSh-1071.2008.1]
Funding-Text	The authors are grateful to R.R. Akopyan, A.G. Babenko, and P.Yu. Glazyrina for careful reading of the manuscript and useful discussions. This work was supported by the Russian Foundation for Basic Research (project No. 08-01-00213) and by the Program for State Support of Leading Scientific Schools of the Russian Federation (project No. NSh-1071.2008.1).
Number-of-Cited-References	17
Usage-Count-Since-2013	3
Journal-ISO	J. Approx. Theory
Doc-Delivery-Number	672EA