APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS
In the class of functions analytic in the annulus \(C_r:=\left\{z\in\mathbb{C}\, :\, r<|z|<1\right\}\) with bounded \(L^p\)-norms on the unit circle, we study the problem of the best approximation of the operator taking the nontangential limit boundary values of a function on the circle \(\Gam...
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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/98 |
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| author | Roman R. Akopyan |
| author_facet | Roman R. Akopyan |
| author_sort | Roman R. Akopyan |
| collection | DOAJ |
| description | In the class of functions analytic in the annulus \(C_r:=\left\{z\in\mathbb{C}\, :\, r<|z|<1\right\}\) with bounded \(L^p\)-norms on the unit circle, we study the problem of the best approximation of the operator taking the nontangential limit boundary values of a function on the circle \(\Gamma_r\) of radius \(r\) to values of the derivative of the function on the circle \(\Gamma_\rho\) of radius \(\rho,\, r<\rho<1,\) by bounded linear operators from \(L^p(\Gamma_r)\) to \(L^p(\Gamma_ \rho)\) with norms not exceeding a number \(N\). A solution of the problem has been obtained in the case when \(N\) belongs to the union of a sequence of intervals. The related problem of optimal recovery of the derivative of a function from boundary values of the function on \(\Gamma_\rho\) given with an error has been solved. |
| format | Article |
| id | doaj-art-1210b51f7a4b475dbed5135d4a1cee87 |
| institution | Matheson Library |
| 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-1210b51f7a4b475dbed5135d4a1cee872025-07-02T02:13:31ZengUral 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.2017.2.00243APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUSRoman R. Akopyan0Ural Federal University; Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, EkaterinburgIn the class of functions analytic in the annulus \(C_r:=\left\{z\in\mathbb{C}\, :\, r<|z|<1\right\}\) with bounded \(L^p\)-norms on the unit circle, we study the problem of the best approximation of the operator taking the nontangential limit boundary values of a function on the circle \(\Gamma_r\) of radius \(r\) to values of the derivative of the function on the circle \(\Gamma_\rho\) of radius \(\rho,\, r<\rho<1,\) by bounded linear operators from \(L^p(\Gamma_r)\) to \(L^p(\Gamma_ \rho)\) with norms not exceeding a number \(N\). A solution of the problem has been obtained in the case when \(N\) belongs to the union of a sequence of intervals. The related problem of optimal recovery of the derivative of a function from boundary values of the function on \(\Gamma_\rho\) given with an error has been solved.https://umjuran.ru/index.php/umj/article/view/98Best approximation of operators, Optimal recovery, Analytic functions |
| spellingShingle | Roman R. Akopyan APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS Ural Mathematical Journal Best approximation of operators, Optimal recovery, Analytic functions |
| title | APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS |
| title_full | APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS |
| title_fullStr | APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS |
| title_full_unstemmed | APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS |
| title_short | APPROXIMATION OF THE DIFFERENTIATION OPERATOR ON THE CLASS OF FUNCTIONS ANALYTIC IN AN ANNULUS |
| title_sort | approximation of the differentiation operator on the class of functions analytic in an annulus |
| topic | Best approximation of operators, Optimal recovery, Analytic functions |
| url | https://umjuran.ru/index.php/umj/article/view/98 |
| work_keys_str_mv | AT romanrakopyan approximationofthedifferentiationoperatorontheclassoffunctionsanalyticinanannulus |