In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin Carathéodory in 1912. The uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically in terms of the limiting behaviour of the images of the functions. The kernel theorem has wide application in the theory of univalent functions and in particular provides the geometric basis for the Loewner differential equation.
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| - Carathéodory kernel theorem (en)
- Теорема Каратеодорі про ядро (uk)
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| - In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin Carathéodory in 1912. The uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically in terms of the limiting behaviour of the images of the functions. The kernel theorem has wide application in the theory of univalent functions and in particular provides the geometric basis for the Loewner differential equation. (en)
- Теорема Каратеодорі про ядро твердження у комплексному аналізі і геометричній теорії функцій доведене грецьким математиком Костянтином Каратеодорі у 1912 році. Теорема має багато застосувань у теорії однолистих функцій. (uk)
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| - In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin Carathéodory in 1912. The uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically in terms of the limiting behaviour of the images of the functions. The kernel theorem has wide application in the theory of univalent functions and in particular provides the geometric basis for the Loewner differential equation. (en)
- Теорема Каратеодорі про ядро твердження у комплексному аналізі і геометричній теорії функцій доведене грецьким математиком Костянтином Каратеодорі у 1912 році. Теорема має багато застосувань у теорії однолистих функцій. (uk)
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