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Bitangential interpolation for upper triangular operators

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Topics in Interpolation Theory

Part of the book series: Operator Theory Advances and Applications ((OT,volume 95))

Abstract

This paper deals with bitangential interpolation problems of the Nevanlinna-Pick type in the general setting of upper triangular operators. (In this setting upper triangular operators play the role of analytic functions and the classical cases emerge by restricting these operators to be Toeplitz.) The approach is based largely on adapting ideas which were introduced by Kat-snelson, Kheifets and Yuditskii, and then further refined by Kheifets, (to establish the existence of and representation formulas for the solutions to a number of interpolation problems in settings based on the usual notion of analyticity) to the setting of upper triangular operators.

One advantage of this approach is that it yields a description of all the solutions to the interpolation problem under consideration in terms of a linear fractional representation of the Redheffer type even when the Pick operator associated with the problem is only positive semidefinite.

The author wishes to express his thanks to Renee and Jay Weiss for endowing the chair which supports his research.

The author wishes to express his thanks to Renee and Jay Weiss for endowing the chair which supports his research.

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Dym, H., Freydin, B. (1997). Bitangential interpolation for upper triangular operators. In: Dym, H., Katsnelson, V., Fritzsche, B., Kirstein, B. (eds) Topics in Interpolation Theory. Operator Theory Advances and Applications, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8944-5_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8944-5_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9838-6

  • Online ISBN: 978-3-0348-8944-5

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