THE BACKUS-GILBERT INVERSION METHOD AND THE PROCESSING OF SAMPLED-DATA

In this note, we show a sequence of interpolation formulas for the Bac kus-Gilbert (BG(;) method with delta-function kernels and penalty func tions J(t. t') = (t - t')(2k) for integers k > 0. We show that the int erpolation in the limit sense of k --> infinity is the Near representa tion. The interpolation formulas are generalizations of the one obtain ed by Caccin ct al. We also investigate the possibility of the BG meth od with delta-function kernels so that it is exactly the same as the S hannon sampling formula.