Metric Constrained Interpolation, Commutant Lifting and Systems

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This book offers a unified approach to both stationary and nonstationary interpolation problems in finite or infinite dimensions, utilizing the commutant lifting theorem from operator theory and the state space method from mathematical system theory. The authors initially aimed to address nonstationary interpolation issues of Nevanlinna-Pick and Nehari types by transforming these problems into stationary ones for operator-valued functions with operator arguments, employing classical commutant lifting techniques. This reduction necessitated a review and further development of classical results for stationary problems within a broader framework. System theory proved essential for structuring the problems and providing natural state space formulas for the solutions. Consequently, the scope of the research expanded beyond the original intent. The final results of this extensive effort are compiled here. The research, initiated in 1994 with financial support from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands, was also bolstered by contributions from Indiana University, Purdue University, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. Special thanks are extended to Dr. A. L. Sakhnovich for his thorough review of the manuscript and to Sharon Wise for her meticulous preparation of the troff file.