An extremal problem for algebraic polynomials with zero mean value on an interval / Arestov VV,Raevskaya VY // MATHEMATICAL NOTES. - 1997. - V. 62, l. 3-4. - P. 278-287.

ISSN/EISSN:

0001-4346 / нет данных

Type:

Article

Abstract:

Let P-n(o)(h) be the set of algebraic polynomials of degree n with real coefficients and with zero mean value (with weight h) on the interval {[}-1, 1]: integral(-1)(1) h(x)p(n)(x) dx = 0; here h is a function which is summable, nonnegative, and nonzero on a set of positive measure on {[}-1, 1]. We study the problem of the least possible value i(n)(h) = inf\{mu(p(n)) : p(n) is an element of p(n)(o)\} of the measure mu(p(n)) = mes\{x is an element of {[}-1, 1] : p(n)(x) greater than or equal to 0\} of the set of points of the interval at which the polynomial p(n) is an element of p(n)(o) nonnegative. We find the exact value of i(n)(h) under certain restrictions on the weight h. In particular, the Jacobi weight h((alpha,beta))(x) = (1 - x)(alpha)(1 + x)(beta) satisfies these restrictions provided that -1 < alpha, beta less than or equal to 0.

Author keywords:

extremal problem; algebraic polynomials; polynomials with zero mean; Jacobi weight

DOI:

10.1007/BF02360868

Web of Science ID:

ISI:000072500900002

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	SEP-OCT
Publisher	PLENUM PUBL CORP
Address	CONSULTANTS BUREAU, 233 SPRING ST, NEW YORK, NY 10013 USA
Language	English
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Number-of-Cited-References	9
Journal-ISO	Math. Notes
Doc-Delivery-Number	ZB721