scholarly journals On the automorphisms of the spectral unit ball

2003 ◽  
Vol 155 (3) ◽  
pp. 207-230 ◽  
Author(s):  
Jérémie Rostand
Keyword(s):  
Unit Ball ◽  
Spectral Unit Ball

Holomorphic Self-Maps of the Spectral unit Ball

1991 ◽  
Vol 23 (3) ◽  
pp. 256-262 ◽  
Author(s):  
T. J. Ransford ◽  
M. C. White
Keyword(s):  
Unit Ball ◽  
Spectral Unit Ball

scholarly journals A local form for the automorphisms of the spectral unit ball

2008 ◽  
Vol 59 (3) ◽  
pp. 321-324 ◽  
Author(s):  
Pascal J. Thomas
Keyword(s):  
Unit Ball ◽  
Local Form ◽  
Spectral Unit Ball

scholarly journals On the zero set of the Kobayashi–Royden pseudometric of the spectral unit ball

2008 ◽  
Vol 93 (1) ◽  
pp. 53-68
Author(s):  
Nikolai Nikolov ◽  
Pascal J. Thomas
Keyword(s):  
Unit Ball ◽  
Zero Set ◽  
Spectral Unit Ball

scholarly journals Certain non-homogeneous matricial domains and Pick–Nevanlinna interpolation problem

2021 ◽  
pp. 2150083
Author(s):  
Vikramjeet Singh Chandel
Keyword(s):  
Automorphism Group ◽  
Unit Ball ◽  
Complex Plane ◽  
Unit Disc ◽  
Interpolation Problem ◽  
Necessary Conditions ◽  
Holomorphic Automorphism ◽  
Spectral Unit Ball ◽  
Holomorphic Automorphism Group

In this paper, 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 [Formula: see text]-point and [Formula: see text]-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.

Holomorphically embedded discs with rapidly growing area

1999 ◽  
Vol 129 (2) ◽  
pp. 343-349
Author(s):  
Josip Globevnik
Keyword(s):  
Unit Ball ◽  
Open Unit ◽  
Open Unit Ball

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.

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