Geometry of the symmetrized polydisc

2004/02/03 by A. Edigarian, Edigarian, A., W. Zwonek +1 · 4 citations
Mathematics · #32A25 #32H35 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32A25 #msc:32H35

paper · pdf · doi:10.48550/arxiv.math/0402033

9 pages

arxiv created 2004/02/03 · arxiv updated 2009/12/01

Abstract

We describe all proper holomorphic mappings of the symmetrized polydisc and study its geometric properties. We also apply the obtained results to the study of the spectral unit ball in \MM_n(\CCⁿ).

Cited by

• Few maps in the rich structure for the domains G_E(3;3;1,1,1) and G_E(3;2;1,2)
• Admissible Fundamental Operators and Models for Γ_{E(3; 3; 1, 1, 1)}-contraction and Γ_{E(3; 2; 1, 2)}-contraction
• Operators on Hilbert Space having Γ_{E(3; 3; 1, 1, 1)} and Γ_{E(3; 2; 1, 2)} as Spectral Sets
• The Hexablock: a domain associated with the μ-synthesis in M₂(\mathbb C)

Related

• Characterizations of Symmetrized Polydisc
• Rank of the derivative of the projection to symmetrized polydisc
• Algebraic Properties of Toeplitz operators on the symmetrized polydisk
• Holomorphic isometries between products of complex unit balls
• A Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball