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arXiv · 2009.01834

Certain non-homogeneous matricial domains and Pick-Nevanlinna interpolation problem

Vikramjeet Singh Chandel
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Abstract

In this article, we consider certain matricial domains that are naturally associated to a given domain of the complex plane. A particular example of such domains is the spectral unit ball. We present several results for these matricial domains. Our first result shows, generalizing a result of Ransford-White for the spectral unit ball, that the holomorphic automorphism group of these matricial domains does not act transitively. We also consider $2$-point and $3$-point Pick-Nevanlinna interpolation problem from the unit disc to these matricial domains. We present results providing necessary conditions for the existence of a holomorphic interpolant for these problems. In particular, we shall observe that these results are generalizations of the results provided by Bharali and Chandel related to these problems.

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Vikramjeet Singh Chandel. 2021-07-07. Certain non-homogeneous matricial domains and Pick-Nevanlinna interpolation problem. https://arxiv.org/abs/2009.01834

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