Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Basel AG
About this chapter
Cite this chapter
Foias, C., Frazho, A.E., Gohberg, I., Kaashoek, M.A. (1998). Interpolation Problems for Operator-Valued Functions. In: Metric Constrained Interpolation, Commutant Lifting and Systems. Operator Theory Advances and Applications, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8791-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8791-5_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9775-4
Online ISBN: 978-3-0348-8791-5
eBook Packages: Springer Book Archive