ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES
The existence and uniqueness of an interpolating periodic spline defined on an equidistant mesh by the linear differential operator \({\cal L}_{2n+2}(D)=D^{2}(D^{2}+1^{2})(D^{2}+2^{2})\cdots (D^{2}+n^{2})\) with \(n\in\mathbb{N}\) are reproved under the final restriction on the step of the mesh. Und...
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| Format: | Article |
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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/88 |
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| _version_ | 1849407526921043968 |
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| author | Sergey I. Novikov |
| author_facet | Sergey I. Novikov |
| author_sort | Sergey I. Novikov |
| collection | DOAJ |
| description | The existence and uniqueness of an interpolating periodic spline defined on an equidistant mesh by the linear differential operator \({\cal L}_{2n+2}(D)=D^{2}(D^{2}+1^{2})(D^{2}+2^{2})\cdots (D^{2}+n^{2})\) with \(n\in\mathbb{N}\) are reproved under the final restriction on the step of the mesh. Under the same restriction, sharp estimates of the error of approximation by such interpolating periodic splines are obtained. |
| format | Article |
| id | doaj-art-b1a05f11ff1c4bf6b93bf1429a47df18 |
| 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-b1a05f11ff1c4bf6b93bf1429a47df182025-08-20T03:36:02ZengUral 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.2017.2.00944ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINESSergey I. Novikov0Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, EkaterinburgThe existence and uniqueness of an interpolating periodic spline defined on an equidistant mesh by the linear differential operator \({\cal L}_{2n+2}(D)=D^{2}(D^{2}+1^{2})(D^{2}+2^{2})\cdots (D^{2}+n^{2})\) with \(n\in\mathbb{N}\) are reproved under the final restriction on the step of the mesh. Under the same restriction, sharp estimates of the error of approximation by such interpolating periodic splines are obtained.https://umjuran.ru/index.php/umj/article/view/88Splines, Interpolation, Approximation, Linear differential operator. |
| spellingShingle | Sergey I. Novikov ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES Ural Mathematical Journal Splines, Interpolation, Approximation, Linear differential operator. |
| title | ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES |
| title_full | ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES |
| title_fullStr | ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES |
| title_full_unstemmed | ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES |
| title_short | ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES |
| title_sort | on interpolation by almost trigonometric splines |
| topic | Splines, Interpolation, Approximation, Linear differential operator. |
| url | https://umjuran.ru/index.php/umj/article/view/88 |
| work_keys_str_mv | AT sergeyinovikov oninterpolationbyalmosttrigonometricsplines |