"Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals"Priyanka, KumariThis work focuses on 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. We introduced a new type of polynomials based on derivative samples, which is different from the Euler-Frobenius polynomials for the multiplicity r > 1. We have provided a complete characterization of uniform sampling with derivatives using Laurent operators. We have discussed the rate of approximation of a signal (not necessarily continuous) by the derivative sampling expansions in shift-invariant spaces generated by compactly supported functions in terms of L^p- average modulus of smoothness. Finally, We have discussed several typical examples illustrating the various problems. |
« back