Abstract
The family of all solutions of the three chains completion problem with a prescribed tolerance is described explicitly. It is shown that this family can be parameterized by a natural set of contractive upper triangular operators. As an application all solutions to a suboptimal nonstationary Nehari problem are described.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arveson, W.B., Interpolation in nest algebras,J. Funct. Anal. 20 (1975), 208–233.
Foias, C., and A.E. Frazho,The commutant lifting approach to interpolation problems, Operator Theory: Advances and Applications, Vol.44, Birkhäuser Verlag, Basel, 1990.
Foias, C., A.E. Frazho, I. Gohberg, and M.A. Kaashoek, Discrete time-variant interpolation as classical interpolation with an operator argument,Integral Equations and Operator Theory 26 (1996), 371–403.
Foias, C., A.E. Frazho, I. Gohberg, and M.A. Kaashoek, A time-variant version of the commutant lifting theorem and nonstationary interpolation problems,Integral Equations and Operator Theory 28 (1997), 158–190.
Frazho, A.E., and S.M. Kherat, Applications of the Schur algorithm to mixedH 2 andH ∞ Nehari problems,J. Math. Anal. Appl. 178 (1993), 488–508.
Gohberg, I., S. Goldberg, and M.A. Kaashoek,Classes of linear operators, Vol. II, Operator Theory: Advances and Applications, Vol.63, Birkhäuser Verlag, Basel, 1993.
Gohberg, I., M.A. Kaashoek and H.J. Woerdeman, The band method for positive and contractive extension problems: An alternative version and new applications,Integral Equations and Operator Theory 12 (1989), 343–382.
Gohberg, I., M.A. Kaashoek and H.J. Woerdeman, The time variant extension problems of Nehari type and the band method. In:H ∞-Control Theory (Eds. E. Mosca, L. Pandolphi), Lecture Notes in Mathematics1496, Springer-Verlag, 1991; pp 309–323.
Gohberg, I., M.A. Kaashoek, and F. van Schagen, Rational contractive and unitary interpolants in realized form,Integral Equations and Operator Theory 11 (1988), 105–127.
Parrott, S., On a quotient norm and the Sz.-Nagy-Foias lifting theorem,J. Funct. Anal. 30 (1978), 311–328.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Foias, C., Frazho, A.E., Gohberg, I. et al. Parameterization of all solutions of the three chains completion problem. Integr equ oper theory 29, 455–490 (1997). https://doi.org/10.1007/BF01193812
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01193812