A class of linear fractional maps of the ball and their composition operators
type: Item
instance of: scholarly article
title: A class of linear fractional maps of the ball and their composition operators
zbMATH Open document ID: 1112.32002
published in: Advances in Mathematics
publication date: 2007-02-26T00:00:00Z
review text: Let \(A = (a_{i,j})\) be an \(N \times N\)-matrix, \(B + (b_j), \mathbb C = (c_j)\) be \(N\)-column vectors, and \(d\) be a complex number. A linear fractional map of \(\mathbb C^n\) is a map of the form \[ u(z) = \frac{Az + B}{\langle z,\overline{\mathbb C}\rangle + d}, \] where \(\langle.,.\rangle\) is the Hermitian product in \(\mathbb C^n.\) The author investigates properties of linear fractional self-maps of the ball that are a generalization of parabolic non-automorphism of the unit disk. So he establishes a normal form of these maps (Theorem 3.1) and gives some applications.
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 5129764
zbMATH Keywords: linear maps
zbMATH Keywords: holomorphic self-maps
zbMATH Keywords: hypercyclic operators
author: Frédéric Bayart
reviewed by: P. Z. Agranovich
MaRDI profile type: Publication
full work available at URL: j.aim.2006.05.012
OpenAlex ID: W1963884035
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DOI: 10.1016/J.AIM.2006.05.012
description: scientific article; zbMATH DE number 5129764