Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials
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.
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-03-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.032 |
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doaj-4d6bd7a1efdf49c99574a4dfba23b2932020-11-24T23:09:42ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-03-015032Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber PolynomialsHelene AiraultWe 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. http://dx.doi.org/10.3842/SIGMA.2009.032vector fieldsunivalent functionsFaber polynomials |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Helene Airault |
| spellingShingle |
Helene Airault Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials Symmetry, Integrability and Geometry: Methods and Applications vector fields univalent functions Faber polynomials |
| author_facet |
Helene Airault |
| author_sort |
Helene Airault |
| title |
Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials |
| title_short |
Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials |
| title_full |
Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials |
| title_fullStr |
Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials |
| title_full_unstemmed |
Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials |
| title_sort |
vector fields on the space of functions univalent inside the unit disk via faber polynomials |
| publisher |
National Academy of Science of Ukraine |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| issn |
1815-0659 |
| publishDate |
2009-03-01 |
| description |
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. |
| topic |
vector fields univalent functions Faber polynomials |
| url |
http://dx.doi.org/10.3842/SIGMA.2009.032 |
| work_keys_str_mv |
AT heleneairault vectorfieldsonthespaceoffunctionsunivalentinsidetheunitdiskviafaberpolynomials |
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1725609852691021824 |