2020/09/03 by Vikramjeet Singh Chandel, Chandel, Vikramjeet Singh
Mathematics · #30E05 #47A56 #47A60 #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primary: 32H35 #Secondary: 32F45
paper · pdf · doi:10.48550/arxiv.2009.01834
openalex publication_date 2020/09/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this article, we consider certain matricial domains that are naturally\nassociated to a given domain of the complex plane. A particular example of such\ndomains is the spectral unit ball. We present several results for these\nmatricial domains. Our first result shows, generalizing a result of\nRansford-White for the spectral unit ball, that the holomorphic automorphism\ngroup of these matricial domains does not act transitively. We also consider\n2-point and 3-point Pick-Nevanlinna interpolation problem from the unit\ndisc to these matricial domains. We present results providing necessary\nconditions for the existence of a holomorphic interpolant for these problems.\nIn particular, we shall observe that these results are generalizations of the\nresults provided by Bharali and Chandel related to these problems.\n