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Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class

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Topics in Interpolation Theory

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

Abstract

An abstract moment problem (which includes the Stieltjes moment problem and the Nevanlinna-Pick problem as typical representatives) is formulated as an integral representation problem. Potapov’s method is used to show that this problem is solvable if and only if two associated Pick operators are nonnegative, or equivalently if and only if a pair of fundamental matrix inequalities are satisfied. The general solution is described in terms of a linear fractional transformation in the nonsingular case.

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References

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© 1997 Springer Basel AG

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Dyukarev, Y.M. (1997). Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class. 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_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8944-5_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9838-6

  • Online ISBN: 978-3-0348-8944-5

  • eBook Packages: Springer Book Archive

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