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arXiv · 2402.08977

Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals

Kumari Priyanka·A. Antony Selvan
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Abstract

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.

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Kumari Priyanka, A. Antony Selvan. 2024-02-14. Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals. https://arxiv.org/abs/2402.08977

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