A Schwarz lemma for a domain related to mu-synthesis

Abstract

We prove a Schwarz lemma for a domain E in 3-dimensional complex space that arises in connection with a problem in H infinity control theory. We describe a class of automorphisms of E and determine the distinguished boundary of E. We obtain a type of Schwarz-Pick lemma for a two by two mu-synthesis problem.

33 pages, 1 figure, This version (v3) contains a correction of inaccuracies in Theorems 2.2 and 2.4. Three of the eleven equivalent conditions we gave for membership of the tetrablock were incorrect. The error does not affect any of the rest of the paper

References in corpus (2)

• The automorphism group of the tetrablock
• Nonisotropically balanced domains, Lempert function estimates, and the spectral Nevanlinna-Pick problem

Cited by in corpus (3)

• The automorphism group of the tetrablock
• The complex geomety of a domain related to $\mu$-synthesis
• A Geometric Characterization of the Symmetrized Bidisc