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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive
SIGMA, 2009 Volume 5, 032, 11 pp. (Mi sigma378)
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

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.

Keywords: vector fields; univalent functions; Faber polynomials.

MSC: 17B66; 33C80; 35A30

Received: July 17, 2008; in final form March 7, 2009; Published online March 15, 2009

Language: English

DOI: 10.3842/SIGMA.2009.032



Bibliographic databases:
ArXiv: 0903.2647

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