Fredholm operator

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• Fredholm-Operator — In der Funktionalanalysis, einem Teilgebiet der Mathematik, ist die Klasse der Fredholm Operatoren (nach E. I. Fredholm) ein bestimmte Klasse linearer Operatoren, die man „fast“ invertieren kann. Jedem Fredholm Operator ordnet man eine ganze Zahl …   Deutsch Wikipedia

• Fredholm operator — In mathematics, a Fredholm operator is an operator that arises in the Fredholm theory of integral equations. It is named in honour of Erik Ivar Fredholm. A Fredholm operator is a bounded linear operator between two Banach spaces whose range is… …   Wikipedia

• Fredholm theory — In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm s theory is… …   Wikipedia

• Fredholm-Index — In der Funktionalanalysis, einem Teilgebiet der Mathematik, ist der Begriff des Fredholm Operators (nach E. I. Fredholm) eine Verallgemeinerung der Invertierbarkeit einer linearen Abbildung zwischen Vektorräumen. Für Fredholm Operatoren kann der… …   Deutsch Wikipedia

• Fredholm determinant — In mathematics, the Fredholm determinant is a complex valued function which generalizes the determinant of a matrix. It is defined for bounded operators on a Hilbert space which differ from the identity operator by a trace class operator. The… …   Wikipedia

• Fredholm kernel — In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space. They are an abstraction of the idea of the Fredholm integral equation and the Fredholm operator, and are one …   Wikipedia

• Fredholm alternative — In mathematics, the Fredholm alternative, name after Ivar Fredholm, is one of Fredholm s theorems and is a result in Fredholm theory. It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a… …   Wikipedia

• Fredholm integral equation — In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. Equation of the first… …   Wikipedia

• Fredholm's theorem — In mathematics, Fredholm s theorems are a set of celebrated results of Ivar Fredholm in the Fredholm theory of integral equations. There are several closely related theorems, which may be stated in terms of integral equations, in terms of linear… …   Wikipedia

• Operator theory — In mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators. Operator theory also includes the study of algebras of operators. Contents …   Wikipedia

• Operator K-theory — In mathematics, operator K theory is a variant of K theory on the category of Banach algebras (In most applications, these Banach algebras are C* algebras). Its basic feature that distinguishes it from algebraic K theory is that it has a Bott… …   Wikipedia