The theory of interpolation with metric constraints started in the beginning of this century with papers of Carathéodory ,  and Schur , , and was continued by Nevanlinna  and Pick , , and then later in the fifties by Nehari . At the end of the sixties and in the beginning of the seventies operator theoretical methods for solving these classical function theory interpolation problems were discovered. The most important developments started with the papers Adamjan-Arov-Krein , Sarason , and Sz.-Nagy-Foias , . In particular, in 1967 Sarason  encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, Sz.-Nagy-Foias ,  derived a purely geometrical extension of Sarason’s results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries, and this work formed the basis of a new method to deal with metric constrained interpolation problems, which usually is referred to as the commutant lifting approach.
KeywordsInterpolation Problem Commutant Lift State Space Solution Nehari Problem Commutant Lift Theorem
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