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Holomorpher Funktionalkalkül Calcul fonctionnel holomorphe Holomorphic functional calculus Càlcul funcional holomorf
rdfs:comment
Der holomorphe Funktionalkalkül ist eine grundlegende Methode aus der mathematischen Theorie der Banachalgebren. Grob gesprochen werden bei diesem Funktionalkalkül Elemente einer -Banachalgebra in holomorphe Funktionen, die in einer Umgebung des Spektrums des Elementes definiert sind, eingesetzt, wodurch das Einsetzen in Polynome verallgemeinert wird. En mathématiques, et plus précisément en analyse, le calcul fonctionnel holomorphe désigne l'application du calcul fonctionnel aux fonctions holomorphes, c'est-à-dire qu'étant donnés une fonction holomorphe ƒ de la variable complexe z et un opérateur linéaire T, l'objectif est de construire un opérateur f (T) étendant ƒ de manière « naturelle ». In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function f of a complex argument z and an operator T, the aim is to construct an operator, f(T), which naturally extends the function f from complex argument to operator argument. More precisely, the functional calculus defines a continuous algebra homomorphism from the holomorphic functions on a neighbourhood of the spectrum of T to the bounded operators. En matemàtiques, el càlcul funcional holomorf és el amb funcions holomorfes. És a dir, donats una funció holomorfa f d'argument complex z i un operador T, l'objectiu és construir un operador, f(T), que estengui la funció f d'un argument complex a un argument operador. Aquest article discuteix el cas en què T és un en un espai de Banach. En particular, T pot ser una matriu quadrada a entrades complexes, un cas que usarem per il·lustrar el càlcul funcional i proporcionar algunes indicacions heurístiques per les suposicions que intervenen en la construcció general.
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January 2017
dbp:reason
This is an incorrect claim, unless we also require that U contain the image of a homotopy from Gamma to Omega.
dbo:abstract
In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function f of a complex argument z and an operator T, the aim is to construct an operator, f(T), which naturally extends the function f from complex argument to operator argument. More precisely, the functional calculus defines a continuous algebra homomorphism from the holomorphic functions on a neighbourhood of the spectrum of T to the bounded operators. This article will discuss the case where T is a bounded linear operator on some Banach space. In particular, T can be a square matrix with complex entries, a case which will be used to illustrate functional calculus and provide some heuristic insights for the assumptions involved in the general construction. En matemàtiques, el càlcul funcional holomorf és el amb funcions holomorfes. És a dir, donats una funció holomorfa f d'argument complex z i un operador T, l'objectiu és construir un operador, f(T), que estengui la funció f d'un argument complex a un argument operador. Aquest article discuteix el cas en què T és un en un espai de Banach. En particular, T pot ser una matriu quadrada a entrades complexes, un cas que usarem per il·lustrar el càlcul funcional i proporcionar algunes indicacions heurístiques per les suposicions que intervenen en la construcció general. Der holomorphe Funktionalkalkül ist eine grundlegende Methode aus der mathematischen Theorie der Banachalgebren. Grob gesprochen werden bei diesem Funktionalkalkül Elemente einer -Banachalgebra in holomorphe Funktionen, die in einer Umgebung des Spektrums des Elementes definiert sind, eingesetzt, wodurch das Einsetzen in Polynome verallgemeinert wird. En mathématiques, et plus précisément en analyse, le calcul fonctionnel holomorphe désigne l'application du calcul fonctionnel aux fonctions holomorphes, c'est-à-dire qu'étant donnés une fonction holomorphe ƒ de la variable complexe z et un opérateur linéaire T, l'objectif est de construire un opérateur f (T) étendant ƒ de manière « naturelle ». Le cas le plus fréquent est celui où T est un opérateur borné sur un espace de Banach. En particulier, en dimension finie, T peut être identifié à une matrice carrée à coefficients complexes ; ce cas permet d'illustrer les idées du calcul fonctionnel, et sert souvent de motivation heuristique aux techniques d'analyse d'opérateurs plus généraux
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