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. It...

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....

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...

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...

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

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...

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

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...

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

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...

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

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

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

operators. This extension is called the Toeplitz extension. By Atkinson's theorem, an element of the Toeplitz algebra Tf + K is a Fredholm operator if...

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...

abstract elliptic operator introduced by Atiyah (1970). If A is an involutive algebra over the complex numbers C, then a Fredholm module over A consists...

class of operators known as Hilbert–Schmidt operators that are especially important in the study of integral equations. Fredholm operators differ from...

compactness assumption is removed, operators need not have countable spectrum in general. Fredholm operator – Part of Fredholm theories in integral equations...

taking Fredholm index as follows. In the even case, each projection e in A decomposes as e0 ⊕ e1 under the grading and e1Fe0 becomes a Fredholm operator from...

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

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...

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

T_{g}-\lambda } is Fredholm if and only if λ {\displaystyle \lambda } is not in the set g ( S 1 ) {\displaystyle g(S^{1})} . If it is Fredholm, its index is...

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

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

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

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...