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This book presents a unified approach for solving both stationary
and nonstationary interpolation problems, in finite or infinite
dimensions, based on the commutant lifting theorem from operator
theory and the state space method from mathematical system theory.
Initially the authors planned a number of papers treating
nonstationary interpolation problems of Nevanlinna-Pick and Nehari
type by reducing these nonstationary problems to stationary ones
for operator-valued functions with operator arguments and using
classical commutant lifting techniques. This reduction method
required us to review and further develop the classical results for
the stationary problems in this more general framework. Here the
system theory turned out to be very useful for setting up the
problems and for providing natural state space formulas for
describing the solutions. In this way our work involved us in a
much wider program than original planned. The final results of our
efforts are presented here. The financial support in 1994 from the
"NWO-stimulansprogramma" for the Thomas Stieltjes Institute for
Mathematics in the Netherlands enabled us to start the research
which lead to the present book. We also gratefully acknowledge the
support from our home institutions: Indiana University at
Bloomington, Purdue University at West Lafayette, Tel-Aviv
University, and the Vrije Universiteit at Amsterdam. We warmly
thank Dr. A.L. Sakhnovich for his carefully reading of a large part
of the manuscript. Finally, Sharon Wise prepared very efficiently
and with great care the troff file of this manuscript; we are
grateful for her excellent typing.
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