Generalization of the Smirnov Operator and Differential Inequalities for Polynomials
- Authors: Kompaneets E.1, Starkov V.1
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Affiliations:
- Petrozavodsk State University
- Issue: Vol 40, No 12 (2019)
- Pages: 2043-2051
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/206441
- DOI: https://doi.org/10.1134/S1995080219120047
- ID: 206441
Cite item
Abstract
The question raised in this article goes back to the problem posed by the famous chemist D. I. Mendeleev in 1887 (solved by A. A. Markov in 1889). In the next 100 years, the Mendeleev problem was repeatedly modificated and solved. Its essence is in the description of conditions under which the inequality ∣f(z)∣ ≤ ∣F(z)∣ for polynomials f and F and for z from a fixed set implies the inequality ∣L[f](z)∣ ≤ ∣L[F](z)∣ for some differential operator L. In the presented paper, we consider a differential operator of special type and arbitrary order. In particular, we obtain a sharp upper estimate for higher order derivatives of arbitrary polynomial in terms of the polynomial values.
Keywords
About the authors
E. Kompaneets
Petrozavodsk State University
Author for correspondence.
Email: g_ek@inbox.ru
Russian Federation, Petrozavodsk, 185910 Republic of Karelia
V. Starkov
Petrozavodsk State University
Author for correspondence.
Email: VstarV@list.ru
Russian Federation, Petrozavodsk, 185910 Republic of Karelia