POLYNOMIALS LEAST DEVIATING FROM ZERO IN \(L^p(-1;1)\), \(0 \le p \le \infty \), WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS

POLYNOMIALS LEAST DEVIATING FROM ZERO IN \(L^p(-1;1)\), \(0 \le p \le \infty \), WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS

We study Chebyshev's problem on polynomials that deviate least from zero with respect to \(L^p\)-means on the interval \([-1;1]\) with a constraint on the location of roots of polynomials. More precisely, we consider the problem on the set \(\mathcal{P}_n(D_R)\) of polynomials of degree \(n\) t...

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Bibliographic Details
Main Author: Alena E. Rokina
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2023-12-01
Series:Ural Mathematical Journal
Subjects:
algebraic polynomials, chebyshev polynomials, constraints on the roots of a polynomial
Online Access:https://umjuran.ru/index.php/umj/article/view/674
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