Classification of semigroups of linear fractional maps in the unit ball

DOI10.1016/j.aim.2006.02.010zbMath1127.47038OpenAlexW2165010016MaRDI QIDQ854105

Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal

Publication date: 7 December 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2006.02.010

zbMATH Keywords

fixed pointssemigroupsiteration theorylinear fractional maps

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Groups and semigroups of linear operators (47D03) Linear composition operators (47B33) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Other generalizations of function theory of one complex variable (32A30)

Related Items (19)

A class of linear fractional maps of the ball and their composition operators ⋮ Complex symmetric \(C_0\)-semigroups on the weighted Hardy spaces \(H_\gamma(\mathbb{D})\) ⋮ Compact differences of composition operators in several variables ⋮ Norms and spectral radii of linear fractional composition operators on the ball ⋮ Semigroups of holomorphic functions in the polydisk ⋮ Affine infinitesimal generators of semigroups on the polydisk ⋮ Cyclic behavior of linear fractional composition operators in the unit ball of \(\mathbb C^N\) ⋮ Hyperbolic composition operators on the ball ⋮ Infinitesimal generators associated with semigroups of linear fractional maps ⋮ Valiron's theorem in the unit ball and spectra of composition operators ⋮ Parabolic composition operators on the ball ⋮ Essential normality of linear fractional composition operators in the unit ball of \(\mathbb C^N\) ⋮ A proof of the Muir-Suffridge conjecture for convex maps of the unit ball in \(\mathbb{C}^n\) ⋮ Canonical models for holomorphic iteration ⋮ Unnamed Item ⋮ The range of holomorphic maps at boundary points ⋮ The linear fractional model on the ball ⋮ Spectra of linear fractional composition operators onH²(B_N) ⋮ Linear fractional composition operators on the Dirichlet space in the unit ball

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