Exponentials reproducing subdivision schemes (Q1405732)

Nonstationary schemes may be useful for the processing of signals that are well approximated by exponential polynomials. This paper develops the theoretical basis for exponentials reproducing subdivision schemes. The existence and uniqueness of these schemes, existence of limit rule, and rate of convergence to the limit rule are proved. It is shown that the refinement rules of even-order exponentials reproducing subdivision scheme converges to the Dubuc-Deslauriers interpolatory scheme of the same order.