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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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|
|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|
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