Interpolation Problems for Operator-Valued Functions
This chapter concentrates on the necessary and sufficient conditions for the existence of solutions for classical and modern H∞ interpolation problems. These interpolation problems have their roots deep in classical analysis, and they are introduced here in a sophisticated way for operator valued functions with operator arguments. Included are the Nevanlinna-Pick, Hermite-Fejér, Nehari, Sarason and Nudelman interpolation problems, in their classical and tangential form. Both one sided and two-sided versions are considered. Proofs of the main existence results will be given in the next chapter, based on the commutant lifting theorem.
KeywordsHilbert Space Toeplitz Operator Interpolation Problem Taylor Coefficient Unilateral Shift
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