mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar Fredholm. By...

the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space. The...

Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators...

compact operators is in the theory of integral equations, where integral operators supply concrete examples of such operators. A typical Fredholm integral...

or as a theorem on Fredholm operators. Part of the result states that a non-zero complex number in the spectrum of a compact operator is an eigenvalue....

algebra, or in terms of the Fredholm operator on Banach spaces. The Fredholm alternative is one of the Fredholm theorems. Fredholm's theorem in linear algebra...

Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory...

compact manifold, it follows from the elliptic theory that P is a Fredholm operator: it has finite-dimensional kernel and cokernel. In the study of hyperbolic...

Compact operator Fredholm theory of integral equations Integral operator Fredholm operator Self-adjoint operator Unbounded operator Differential operator Umbral...

is one example of a Fredholm operator; it has Fredholm index −1. Jean Delsarte introduced the notion of generalized shift operator (also called generalized...

the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredholm theory. Fredholm kernels are named...

{\displaystyle T-\lambda I_{X}} is not a Fredholm operator, where I X {\displaystyle I_{X}} denotes the identity operator on X, so that I X ( x ) = x {\displaystyle...

the kernel is then variously referred to as the Fredholm operator, the nuclear operator or the Fredholm kernel. Bateman transform Convolution kernel Circular...

of an operator is precisely the Euler characteristic of the 2-term complex 0 → V → W → 0. In operator theory, the index of Fredholm operators is an object...

noncommutative geometry Fredholm number, in number theory, apparently not in fact studied by Fredholm Fredholm operator, in mathematics Fredholm's theorem, in mathematics...

derivatives. The existence theory for elliptic operators, using Gårding's inequality, Lax–Milgram lemma and Fredholm alternative, states the sufficient condition...

operator topology ultraweak topology Singular value (or S-number) Fredholm operator Fuglede's theorem Compression (functional analysis) Friedrichs extension...

The Fourier operator is the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform, and is a two-dimensional function...

integral Amenable group Banach–Tarski paradox Hausdorff paradox Fredholm equation Fredholm operator Liouville–Neumann series See also list of transforms, list...

mathematics, the Fredholm determinant is a complex-valued function which generalizes the determinant of a finite dimensional linear operator. It is defined...

equation to an integral equation on the boundary to which the theory of Fredholm operators can be applied. The theory is particularly simple in two dimensions—the...

functions. List of transforms List of Fourier-related transforms Transfer operator Fredholm operator Borel transform Glossary of mathematical symbols...

such that A − λ I {\displaystyle A-\lambda I} is not semi-Fredholm. (The operator is semi-Fredholm if its range is closed and either its kernel or cokernel...

The first major use of the resolvent operator as a series in A (cf. Liouville–Neumann series) was by Ivar Fredholm, in a landmark 1903 paper in Acta Mathematica...

differential operator. However, it is an elliptic pseudodifferential operator.) As the elliptic differential operator D has a pseudoinverse, it is a Fredholm operator...

results from applying the resolvent formalism to solve Fredholm integral equations in Fredholm theory. The Liouville–Neumann series is defined as ϕ (...

such as those above also using integral operator notation. For example, we can define the Fredholm integral operator as: ( F y ) ( t ) := ∫ t 0 T K ( t ,...

In operator theory, Atkinson's theorem (named for Frederick Valentine Atkinson) gives a characterization of Fredholm operators. Let H be a Hilbert space...

alternative and, more generally, the Fredholm-type properties of the operator involved. The concept is named after Erik Ivar Fredholm. Let A be a real n × n-matrix...

K-theoretic methods into the study of C*-algebras was the Fredholm index: Given a bounded linear operator on a Hilbert space that has finite-dimensional kernel...