DISPLACEMENT STRUCTURE AND COMPLETION PROBLEMS

A general result is proven concerning time-variant displacement equati ons with positive solutions in a general operatorial setting. It is th en shown that the solutions of several completion problems, recently c onsidered in connection with classical interpolation and moment theory , follow as special cases of the main result. The main purpose of this paper is to show that under supplementary finite-dimensionality condi tions, a so-called generalized Schur algorithm, which naturally arises in connection with displacement equations, can be used to prove the a bove-mentioned result. The associated transmission-line interpretation is also discussed in terms of a cascade of elementary sections with i ntrinsic blocking properties.