Some New Observations on Interpolation in the Spectral Unit Ball

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
Publication:	Integral Equations and Operator Theory
Publisher:	Springer
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.ac.in/id/eprint/14164

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