Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 032, 11 pages      arXiv:0903.2647      https://doi.org/10.3842/SIGMA.2009.032
Contribution to the Special Issue on Kac-Moody Algebras and Applications

Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials

Helene Airault
LAMFA CNRS UMR 6140, Insset, Université de Picardie Jules Verne, 48 rue Raspail, 02100 Saint-Quentin (Aisne), France

Received July 17, 2008, in final form March 07, 2009; Published online March 15, 2009

Abstract
We obtain the Kirillov vector fields on the set of functions f univalent inside the unit disk, in terms of the Faber polynomials of 1/f(1/z). Our construction relies on the generating function for Faber polynomials.

Key words: vector fields; univalent functions; Faber polynomials.

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