A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS

We give a characterization of elements of a subspace of a complex Banach space with the property that the norm of a bounded linear functional on the subspace is attained at those elements. In particular, we discuss properties of polynomials that are extremal in sharp pointwise Nikol'skii inequa...

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Main Author: Vitalii V. Arestov
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 2017-12-01
Series:Ural Mathematical Journal
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Online Access:https://umjuran.ru/index.php/umj/article/view/102
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author Vitalii V. Arestov
author_facet Vitalii V. Arestov
author_sort Vitalii V. Arestov
collection DOAJ
description We give a characterization of elements of a subspace of a complex Banach space with the property that the norm of a bounded linear functional on the subspace is attained at those elements. In particular, we discuss properties of polynomials that are extremal in sharp pointwise Nikol'skii inequalities for algebraic polynomials in a weighted \(L_q\)-space on a finite or infinite interval.
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institution Kabale University
issn 2414-3952
language English
publishDate 2017-12-01
publisher 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
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series Ural Mathematical Journal
spelling doaj-art-11def3d839af434da2ca6983db81d0852025-08-20T03:33:26ZengUral 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 MechanicsUral Mathematical Journal2414-39522017-12-013210.15826/umj.2017.2.00445A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMSVitalii V. Arestov0Ural Federal University, EkaterinburgWe give a characterization of elements of a subspace of a complex Banach space with the property that the norm of a bounded linear functional on the subspace is attained at those elements. In particular, we discuss properties of polynomials that are extremal in sharp pointwise Nikol'skii inequalities for algebraic polynomials in a weighted \(L_q\)-space on a finite or infinite interval.https://umjuran.ru/index.php/umj/article/view/102Complex Banach space, Bounded linear functional on a subspace, Algebraic polynomial, Pointwise Nikol'skii inequality
spellingShingle Vitalii V. Arestov
A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS
Ural Mathematical Journal
Complex Banach space, Bounded linear functional on a subspace, Algebraic polynomial, Pointwise Nikol'skii inequality
title A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS
title_full A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS
title_fullStr A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS
title_full_unstemmed A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS
title_short A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS
title_sort characterization of extremal elements in some linear problems
topic Complex Banach space, Bounded linear functional on a subspace, Algebraic polynomial, Pointwise Nikol'skii inequality
url https://umjuran.ru/index.php/umj/article/view/102
work_keys_str_mv AT vitaliivarestov acharacterizationofextremalelementsinsomelinearproblems
AT vitaliivarestov characterizationofextremalelementsinsomelinearproblems