Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals
<|reference_start|>Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals: 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.<|reference_end|>
@article{priyanka2024derivative,
    title={Derivative sampling expansions in shift-invariant spaces with error
  estimates covering discontinuous signals},
    author={Kumari Priyanka and A. Antony Selvan},
    journal={arXiv preprint arXiv:2402.08977},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08977},
    primaryClass={math.FA cs.IT math.IT}
}