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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 032, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.032 (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
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DOI: https://doi.org/10.3842/SIGMA.2009.032
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.
Received: July 17, 2008; in final form March 7, 2009; Published online March 15, 2009
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Document Type: Article
MSC: 17B66; 33C80; 35A30
Language: English
Citation: Helene Airault, “Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials”, SIGMA, 5 (2009), 032, 11 pp.
Citation in format AMSBIB
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