Fredholm operator information

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...

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

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...

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....

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

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

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...

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

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

{\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...

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...

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

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...

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...

assumption is removed, operators need not have countable spectrum in general. Fredholm operator Singular value decomposition#Bounded operators on Hilbert spaces –...

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...

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

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...

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...