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Kelkaj kompleksaj variabloj Functie van meer complexe variabelen Múltiples variables complejas Function of several complex variables Fonction de plusieurs variables complexes 多変数複素関数 Многомерный комплексный анализ Funzioni di più variabili complesse
rdfs:comment
Многомерный комплексный анализ — раздел математики, изучающий голоморфные функции нескольких комплексных переменных, определенные в многомерном комплексном пространстве, голоморфные отображения и подмногообразия комплексного пространства. Начало систематическому изучению многомерных комплексных функций было положено К. Вейерштрассом и А. Пуанкаре в конце XIX века. А. Пуанкаре распространил на функции нескольких переменных основную теорему Коши и заложил основы многомерной теории вычетов. Методы многомерного комплексного анализа в настоящее время широко применяются в квантовой теории поля, математической физике, дифференциальной и алгебраической геометрии. La théorie des fonctions de plusieurs variables complexes est une branche des mathématiques traitant des fonctions à variables complexes. On définit de cette manière une fonction de Cn dans C, dont on peut noter les variables . L'analyse complexe correspond au cas . La teoria delle funzioni di più variabili complesse è il ramo della matematica che studia le funzioni in più variabili , definite sullo spazio delle ennuple di numeri complessi, , ove n>1, ed a valori nei numeri complessi. Come in analisi complessa, che si occupa del caso molto particolare , non vengono considerate tutte le funzioni, ma solo quelle analitiche, cioè le funzioni che sono rappresentabili localmente come serie di potenze nelle variabili . The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variables (and analytic space), that has become a common name for that whole field of study and Mathematics Subject Classification has, as a top-level heading. A function is n-tuples of complex numbers, classically studied on . Kelkaj kompleksaj variabloj estas matematika kampo en kiu oni studas holomorfajn funkciojn en pli ol unu kompleksa dimensio. 数学における多変数複素関数論(たへんすうふくそかんすうろん、英: the theory of functions of several complex variables)とは、複素多変数の複素数値関数、すなわち、n 個の複素数の組全体のなす数ベクトル空間 Cn 上の複素数値関数 を扱う分野である。複素解析(これは n = 1 の場合に当たる理論ではあるが、n > 1 の場合とは一線を画す性質を持つ)と同様、任意の単なる函数を扱うものではなく、正則 (holomorphic) あるいは複素解析的 (complex analytic) な関数、つまり局所的に変数 zi たちの冪級数で書けるような関数を扱う。そのような関数は結局のところ、多項式列の局所一様極限として得られるような関数ということもでき、n 次元コーシー・リーマンの方程式の局所解と言っても同じことであるということが分かる。 La teoría de funciones de múltiples variables complejas es una rama de las matemáticas que trata sobre las funciones del tipo f(z1, z2, ..., zn) en el espacio Cn de n-tuplas de números complejos. Como en el análisis complejo, que es el caso para n = 1 pero para una variable distinta, estas no son cualquier tipo de función: se supone que son funciones analíticas, de forma tal que en forma local ellas son series de potencias de las variables zi. In de functietheorie, een deelgebied van de wiskunde, houdt de theorie van functies van meer complexe variabelen zich bezig met functies van het type op de ruimte van -tupels van complexe getallen. Net als in de functietheorie, wat het geval als is, maar met een eigen karakter, zijn dit niet zomaar functies: ze worden geacht analytisch te zijn, zodat de functiewaarde lokaal gesproken een machtreeks in de variabelen is.
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August 2021
dbp:reason
it is unclear whether this definition is equivalent with the definition given in the lead of holomorphic function Why defining dz_\lambda, which is not used in the section?
dbp:title
Holomorphically convex Biholomorphic mapping Analytic function biholomorphically equivalent Cousin problems Coherent algebraic sheaf Pseudoconvex Domain of holomorphy Power series Oka theorems Plurisubharmonic function Hartogs theorem Coherent analytic sheaf polydisc Pseudo-convex and pseudo-concave Reinhardt domain Levi pseudoconvex Coherent sheaf exhaustion function Stein manifold
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Holomorphicallyconvex Domainofholomorphy biholomorphicallyequivalent polydisc ReinhardtDomain pseudoconvex ExhaustionFunction Levipseudoconvex
dbo:abstract
数学における多変数複素関数論(たへんすうふくそかんすうろん、英: the theory of functions of several complex variables)とは、複素多変数の複素数値関数、すなわち、n 個の複素数の組全体のなす数ベクトル空間 Cn 上の複素数値関数 を扱う分野である。複素解析(これは n = 1 の場合に当たる理論ではあるが、n > 1 の場合とは一線を画す性質を持つ)と同様、任意の単なる函数を扱うものではなく、正則 (holomorphic) あるいは複素解析的 (complex analytic) な関数、つまり局所的に変数 zi たちの冪級数で書けるような関数を扱う。そのような関数は結局のところ、多項式列の局所一様極限として得られるような関数ということもでき、n 次元コーシー・リーマンの方程式の局所解と言っても同じことであるということが分かる。 La teoria delle funzioni di più variabili complesse è il ramo della matematica che studia le funzioni in più variabili , definite sullo spazio delle ennuple di numeri complessi, , ove n>1, ed a valori nei numeri complessi. Come in analisi complessa, che si occupa del caso molto particolare , non vengono considerate tutte le funzioni, ma solo quelle analitiche, cioè le funzioni che sono rappresentabili localmente come serie di potenze nelle variabili . In de functietheorie, een deelgebied van de wiskunde, houdt de theorie van functies van meer complexe variabelen zich bezig met functies van het type op de ruimte van -tupels van complexe getallen. Net als in de functietheorie, wat het geval als is, maar met een eigen karakter, zijn dit niet zomaar functies: ze worden geacht analytisch te zijn, zodat de functiewaarde lokaal gesproken een machtreeks in de variabelen is. La théorie des fonctions de plusieurs variables complexes est une branche des mathématiques traitant des fonctions à variables complexes. On définit de cette manière une fonction de Cn dans C, dont on peut noter les variables . L'analyse complexe correspond au cas . Kelkaj kompleksaj variabloj estas matematika kampo en kiu oni studas holomorfajn funkciojn en pli ol unu kompleksa dimensio. Многомерный комплексный анализ — раздел математики, изучающий голоморфные функции нескольких комплексных переменных, определенные в многомерном комплексном пространстве, голоморфные отображения и подмногообразия комплексного пространства. Начало систематическому изучению многомерных комплексных функций было положено К. Вейерштрассом и А. Пуанкаре в конце XIX века. А. Пуанкаре распространил на функции нескольких переменных основную теорему Коши и заложил основы многомерной теории вычетов. Методы многомерного комплексного анализа в настоящее время широко применяются в квантовой теории поля, математической физике, дифференциальной и алгебраической геометрии. La teoría de funciones de múltiples variables complejas es una rama de las matemáticas que trata sobre las funciones del tipo f(z1, z2, ..., zn) en el espacio Cn de n-tuplas de números complejos. Como en el análisis complejo, que es el caso para n = 1 pero para una variable distinta, estas no son cualquier tipo de función: se supone que son funciones analíticas, de forma tal que en forma local ellas son series de potencias de las variables zi. The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variables (and analytic space), that has become a common name for that whole field of study and Mathematics Subject Classification has, as a top-level heading. A function is n-tuples of complex numbers, classically studied on . As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that, locally, they are power series in the variables zi. Equivalently, they are locally uniform limits of polynomials; or locally square-integrable solutions to the n-dimensional . For one complex variable, every domain, is the domain of holomorphy of some function, in other words every domain has a function for which it is the domain of holomorphy. For several complex variables, this is not the case; there exist domains that are not the domain of holomorphy of any function, and so is not always the domain of holomorphy, so the domain of holomorphy is one of the themes in this field. Patching the local data of meromorphic functions, i.e. the problem of creating a global meromorphic function from zeros and poles, is called the Cousin problem. Also, the interesting phenomena that occur in several complex variables are fundamentally important to the study of compact complex manifolds and complex projective varieties and has a different flavour to complex analytic geometry in or on Stein manifolds, these are much similar to study of algebraic varieties that is study of the algebraic geometry than complex analytic geometry.
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B.V. V.S. E.M. V.I. A.L. A.A. E.D.
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Onishchik Chirka Danilov Shabat Solomentsev Gonchar Vladimirov
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