Abstract
In this chapter we will use the commutant lifting theorem with the functional model S(m) to solve the Carathéodory, Nevanlinna-Pick, and Hermite-Fejér interpolation problems. Besides this we will present the natural connection between Hermite-Fejér interpolation theory and contractive Hankel operators with rational symbols. In particular, we will solve the Nehari H∞ optimization problem for rational symbols by Hermite-Fejér interpolation. Also we will show how the Hankel operator in the Nehari optimization problem can be used in Hermite-Fejér interpolation. Furthermore we will present state space realization methods for solving the Nehari H∞ optimization problem with rational symbols Finally, we present a Schur-Cohn test based on Hankel operators, and give a geometric interpretation of the norm of Hankel operators with rigid rational symbols.
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Foias, C., Frazho, A.E. (1990). Some Classical Interpolation Problems. In: The Commutant Lifting Approach to Interpolation Problems. OT 44 Operator Theory: Advances and Applications, vol 44. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7712-1_10
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DOI: https://doi.org/10.1007/978-3-0348-7712-1_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7714-5
Online ISBN: 978-3-0348-7712-1
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