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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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
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| 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. |
| format | Article |
| id | doaj-art-11def3d839af434da2ca6983db81d085 |
| 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 |
| record_format | Article |
| 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 |