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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• ISSN: 1815-0659
• Main Author: Airault, H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149172
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials / H. Airault // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ.

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.