Multidimensional analogs of the Fekete--Szegö functional
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929374452776960 |
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| author | Elin, Mark Jacobzon, Fiana |
| author_facet | Elin, Mark Jacobzon, Fiana |
| contents | In this paper we introduce the Fekete--Szegö type mapping in the open unit ball of a complex Banach space. % and study its geometric and analytical properties. All previously studied modifications of the Fekete--Szegö functional are either special cases or `components' of the mapping we introduce.
The study involves the examination of transforms of the Fekete--Szegö mapping under specific transformations applied to given holomorphic mappings.
We show that for a mapping $f$, the third order Fréshet derivative of the inverse mapping $f^{-1}$ and of elements of the semigroup generated by $f$ can be expressed in terms of the Fekete--Szegö mapping. Estimates of the Fekete--Szegö mapping over some subclasses of semigroup generators and of starlike mappings are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multidimensional analogs of the Fekete--Szegö functional Elin, Mark Jacobzon, Fiana Complex Variables In this paper we introduce the Fekete--Szegö type mapping in the open unit ball of a complex Banach space. % and study its geometric and analytical properties. All previously studied modifications of the Fekete--Szegö functional are either special cases or `components' of the mapping we introduce. The study involves the examination of transforms of the Fekete--Szegö mapping under specific transformations applied to given holomorphic mappings. We show that for a mapping $f$, the third order Fréshet derivative of the inverse mapping $f^{-1}$ and of elements of the semigroup generated by $f$ can be expressed in terms of the Fekete--Szegö mapping. Estimates of the Fekete--Szegö mapping over some subclasses of semigroup generators and of starlike mappings are also presented. |
| title | Multidimensional analogs of the Fekete--Szegö functional |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2406.02752 |