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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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