Jacobi translation and the inequality of different metrics for algebraic polynomials on an interval
| Autor: | Vitalii V. Arestov, M. V. Deikalova |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
General Mathematics Operator (physics) 010102 general mathematics 010103 numerical & computational mathematics Interval (mathematics) Translation (geometry) Space (mathematics) 01 natural sciences Combinatorics Translation operator Uniform norm Beta (velocity) 0101 mathematics Mathematics Algebraic polynomial |
| Zdroj: | Doklady Mathematics. 95:21-25 |
| ISSN: | 1531-8362 1064-5624 |
| Popis: | 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 (α,β) , 1 ≤ q −1, is investigated. 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 (α,β) , 1 ≤ q < ∞, $$\alpha > \beta \geqslant - \frac{1}{2}$$ , is attained. |
| Databáze: | OpenAIRE |
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