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 |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
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 |
| Summary: | 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. |
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| ISSN: | 2414-3952 |