Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911776900120576 |
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| author | Priyanka, Kumari Selvan, A. Antony |
| author_facet | Priyanka, Kumari Selvan, A. Antony |
| contents | This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of polynomials based on derivative samples is introduced, which is different from the Euler-Frobenius polynomials for the multiplicity $r>1$. A complete characterization of uniform sampling with derivatives is given using Laurent operators. The rate of approximation of a signal (not necessarily continuous) by the derivative sampling expansions in shift-invariant spaces generated by compactly supported functions is established in terms of $L^p$- average modulus of smoothness. Finally, several typical examples illustrating the various problems are discussed in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08977 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals Priyanka, Kumari Selvan, A. Antony Functional Analysis Information Theory 42C15, 94A20 This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of polynomials based on derivative samples is introduced, which is different from the Euler-Frobenius polynomials for the multiplicity $r>1$. A complete characterization of uniform sampling with derivatives is given using Laurent operators. The rate of approximation of a signal (not necessarily continuous) by the derivative sampling expansions in shift-invariant spaces generated by compactly supported functions is established in terms of $L^p$- average modulus of smoothness. Finally, several typical examples illustrating the various problems are discussed in detail. |
| title | Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals |
| topic | Functional Analysis Information Theory 42C15, 94A20 |
| url | https://arxiv.org/abs/2402.08977 |