## Abstract

In this paper a positive commuting expansion problem is presented and solved. The problem is set up in the framework of a minimal unitary dilation of a contraction acting on a Hilbert space and includes the Carathéodory and other classical interpolation problems. By combining the geometry of the minimal unitary dilation with state space techniques from system theory, a special solution is constructed. Next using the band method approach and spectral factorizations of this special solution a linear fractional parameterization of all solutions is obtained. Explicit state space formulas and applications to some classical interpolation problems are given.

Original language | English |
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Pages (from-to) | 311-371 |

Journal | Integral Equations and Operator Theory |

Volume | 42 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 |