Hermite-type interpolation in terms of exponential polynomials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929624184782848 |
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| author | Ali, Ali Hasan Páles, Zsolt |
| author_facet | Ali, Ali Hasan Páles, Zsolt |
| contents | Motivated by classical results of approximation theory, we define an Hermite-type interpolation in terms of $n$-dimensional subspaces of the space of $n$ times continuously differentiable functions. In the main result of this paper, we establish an error term in integral form for this interpolation in the case when the $n$-dimensional subspace is the kernel of an $n$th order linear differential operator with constant coefficients. Several corollaries are deduced illustrating the applicability of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hermite-type interpolation in terms of exponential polynomials Ali, Ali Hasan Páles, Zsolt Classical Analysis and ODEs 41A05, 41A10, 34B05 Motivated by classical results of approximation theory, we define an Hermite-type interpolation in terms of $n$-dimensional subspaces of the space of $n$ times continuously differentiable functions. In the main result of this paper, we establish an error term in integral form for this interpolation in the case when the $n$-dimensional subspace is the kernel of an $n$th order linear differential operator with constant coefficients. Several corollaries are deduced illustrating the applicability of this result. |
| title | Hermite-type interpolation in terms of exponential polynomials |
| topic | Classical Analysis and ODEs 41A05, 41A10, 34B05 |
| url | https://arxiv.org/abs/2412.07925 |