## Abstract

In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems invariant in one direction. In this paper we extend and solve in the class SI, a number of problems originally set for the class S of functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned signature matrix J. The problems we consider include the Schur algorithm and the Nevanlinna-Pick interpolation problem. The arguments rely on a correspondence between elements in a given subclass of SI and elements in S. Another important tool in the arguments is a new result pertaining to the classical tangential Schur algorithm.

Original language | English |
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Pages (from-to) | 313-344 |

Number of pages | 32 |

Journal | Integral Equations and Operator Theory |

Volume | 74 |

Issue number | 3 |

DOIs | |

State | Published - 1 Nov 2012 |

## Keywords

- Linear differential equations
- Schur algorithm
- Time-invariant 2D-systems