Interpolation formulas for functions of exponential type. (Q1771840)

The authors present derivative-free estimates of the remainder of any interpolation formula of the Lagrange type on the class of functions of the space \(L^2_{(-\infty ,\infty )}\). The nondependence of the estimate on the higher derivatives of the interpolated function is achieved by the assumption that the function under consideration may be extended in the whole complex plane as a holomorphic function of an exponential type. In the second part of the paper, the optimal interpolation rules are constructed via minimization of the above estimates.