Abstract
In this paper the classical interpolation problems of Nevanlinna-Pick and Carathéodory-Fejér, as well as mixtures of the two, are solved in the general setting of upper triangular operators. Herein, the “points” at which the interpolation is carried out are themselves (diagonal) operators, and the components of all the intervening operators in their natural matrix representation may be finite or infinite dimensional. Moreover, we consider both contractive and strictly contractive solutions. A number of classical and new interpolation problems emerge as special cases.
Patrick Dewilde wishes to acknowledge with thanks the support of the Commission of the EEC under the ESPRIT BRA Project NANA (3280) and the Meyerhoff Foundation for a visiting fellowship at the Weizmann Institute.
Harry Dym wishes to thank Renee and Jay Weiss for endowing the chair which supports his research at the Weizmann Institute, and the STW for a visitors’ fellowship at Delft University of Technology under the JEMNA program.
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Dewilde, P., Dym, H. (1992). Interpolation for Upper Triangular Operators. In: Gohberg, I. (eds) Time-Variant Systems and Interpolation. Operator Theory: Advances and Applications, vol 56. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8615-4_5
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DOI: https://doi.org/10.1007/978-3-0348-8615-4_5
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