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Discrete time-variant interpolation as classical interpolation with an operator argument |
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| Authors: | C. Foias A. E. Frazho I. Gohberg M. A. Kaashoek |
| Affiliation: | (1) Department of Mathematics, Indiana University, 47405 Bloomington, IN, USA;(2) School of Aeronautics and Astronautics, Purdue University, 47907 West Lafayette, IN, USA;(3) Raymond and Beverly Sackler Faculty of Exact Sciences School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv, Israel;(4) Faculteit Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands |
| Abstract: | Necessary and sufficient conditions are derived for the existence of solutions to discrete time-variant interpolation problems of Nevanlinna-Pick and Nudelman type. The proofs are based on a reduction scheme which allows one to treat these time-variant interpolation problems as classical interpolation problems for operator-valued functions with operator arguments. The latter ones are solved by using the commutant lifting theorem. |
| Keywords: | primary 47A57, 30E05 secondary 47A20 |
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