Bharali, Gautam
(2007)
*Some New Observations on Interpolation in the Spectral Unit Ball.*
In: Integral Equations and Operator Theory, 59
(3).
pp. 329-343.

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## Abstract

We present several results associated to a holomorphic-interpolation problem for the spectral unit ball \Omega n, n ≥ 2. We begin by showing that a known necessary condition for the existence of a O(D;\Omega n)-interpolant (D here being the unit disc in C), given that the matricial data are non-derogatory, is not sufficient. We provide next a new necessary condition for the solvability of the two-point interpolation problem – one which is not restricted only to non-derogatory data, and which incorporates the Jordan structure of the prescribed data. We then use some of the ideas used in deducing the latter result to prove a Schwarz-type lemma for holomorphic self-maps of \Omega n, n ≥ 2.

Item Type: | Journal Article |
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Related URLs: | |

Additional Information: | Copyright of this article belongs to Springer. |

Keywords: | Complex geometry;Caratheodory metric;minimial polynomial;Schwarz lemma;spectral radius;spectral unit ball. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 04 Jun 2008 |

Last Modified: | 19 Sep 2010 04:45 |

URI: | http://eprints.iisc.ernet.in/id/eprint/14164 |

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