Cousin problems (original) (raw)
In mathematics, the Cousin problems are two questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced in special cases by in 1895. They are now posed, and solved, for any complex manifold M, in terms of conditions on M. For both problems, an open cover of M by sets Ui is given, along with a meromorphic function fi on each Ui.
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| dbo:abstract | In mathematics, the Cousin problems are two questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced in special cases by in 1895. They are now posed, and solved, for any complex manifold M, in terms of conditions on M. For both problems, an open cover of M by sets Ui is given, along with a meromorphic function fi on each Ui. (en) 数学においてクザン問題(英: Cousin problems)とは、局所的データにより特定される有理型函数の存在についての、多変数複素解析函数における2つの問題のことを言う。これらの問題の特殊な場合は、P. クザン(P. Cousin)により1895年に導入された。これらの問題は現在、任意の複素多様体 M に対して、M の条件として解けている。 どちらの問題も、集合 Ui による M の開被覆と、各 Ui 上で与えられた有理型函数 fi に関する問題である。 (ja) 복소기하학에서 쿠쟁 문제(Cousin問題, 영어: Cousin problems)는 복소다양체 위의, 정칙 함수의 층과 유리형 함수의 층 사이의 관계에 대한 두 개의 유명한 문제이다. (ko) Теорема Ока об аппроксимации — теорема о необходимых и достаточных условиях аппроксимации голоморфной функции нескольких комплексных переменных. Сформулирована и доказана в 1939 году. (ru) |
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| dbp:title | Cousin problems (en) |
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| rdfs:comment | In mathematics, the Cousin problems are two questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced in special cases by in 1895. They are now posed, and solved, for any complex manifold M, in terms of conditions on M. For both problems, an open cover of M by sets Ui is given, along with a meromorphic function fi on each Ui. (en) 数学においてクザン問題(英: Cousin problems)とは、局所的データにより特定される有理型函数の存在についての、多変数複素解析函数における2つの問題のことを言う。これらの問題の特殊な場合は、P. クザン(P. Cousin)により1895年に導入された。これらの問題は現在、任意の複素多様体 M に対して、M の条件として解けている。 どちらの問題も、集合 Ui による M の開被覆と、各 Ui 上で与えられた有理型函数 fi に関する問題である。 (ja) 복소기하학에서 쿠쟁 문제(Cousin問題, 영어: Cousin problems)는 복소다양체 위의, 정칙 함수의 층과 유리형 함수의 층 사이의 관계에 대한 두 개의 유명한 문제이다. (ko) Теорема Ока об аппроксимации — теорема о необходимых и достаточных условиях аппроксимации голоморфной функции нескольких комплексных переменных. Сформулирована и доказана в 1939 году. (ru) |
| rdfs:label | Cousin problems (en) クザン問題 (ja) 쿠쟁 문제 (ko) Теорема Ока об аппроксимации (ru) |
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