An algebra of differential operators and generating functions on the set of univalent functions |
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| Authors: | Hé lè ne Airault |
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| Affiliation: | a INSSET, Université de Picardie Jules Verne, 48 rue Raspail, 02100 Saint-Quentin, (Aisne), Laboratoire CNRS FRE 2270, LAMFA (Amiens), France
b Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China |
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| Abstract: | With a method close to that of Kirillov [4], we define sequences of vector fields on the set of univalent functions and we construct systems of partial differential equations which have the sequence of the Faber polynomials (Fn) as a solution. Through the Faber polynomials and Grunsky coefficients, we obtain the generating functions for some of the sequences of vector fields. |
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| Keywords: | 17B66 17B68 33C80 33E30 35A30 |
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