A Naimark dilation perspective of Nevanlinna-Pick interpolation

A.E. Frazho; M.A. Kaashoek

doi:10.1007/s00020-003-1287-z

A Naimark dilation perspective of Nevanlinna-Pick interpolation

A.E. Frazho, M.A. Kaashoek

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

In this paper a positive real tangential Nevanlinna-Pick interpolation problem with interpolation at operator points is solved. The Naimark dilation theorem together with the state space method from systems theory are used to obtain a parameterization for the set of all solutions. Explicit state space formulas are given for both the singular and non-singular case. In the proofs the solution of an intermediate isometric extension problem plays an important role.

Original language	English
Pages (from-to)	323-378
Number of pages	56
Journal	Integral Equations and Operator Theory
Volume	49
Issue number	3
DOIs	https://doi.org/10.1007/s00020-003-1287-z
Publication status	Published - 2004

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MR2068433

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10.1007/s00020-003-1287-z

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title = "A Naimark dilation perspective of Nevanlinna-Pick interpolation",

abstract = "In this paper a positive real tangential Nevanlinna-Pick interpolation problem with interpolation at operator points is solved. The Naimark dilation theorem together with the state space method from systems theory are used to obtain a parameterization for the set of all solutions. Explicit state space formulas are given for both the singular and non-singular case. In the proofs the solution of an intermediate isometric extension problem plays an important role.",

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AU - Kaashoek, M.A.

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AB - In this paper a positive real tangential Nevanlinna-Pick interpolation problem with interpolation at operator points is solved. The Naimark dilation theorem together with the state space method from systems theory are used to obtain a parameterization for the set of all solutions. Explicit state space formulas are given for both the singular and non-singular case. In the proofs the solution of an intermediate isometric extension problem plays an important role.

U2 - 10.1007/s00020-003-1287-z

DO - 10.1007/s00020-003-1287-z

M3 - Article

SN - 0378-620X

VL - 49

SP - 323

EP - 378

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

A Naimark dilation perspective of Nevanlinna-Pick interpolation

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