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...

In mathematics, the analytic Fredholm theorem is a result concerning the existence of bounded inverses for a family of bounded linear operators on a Hilbert...

In this paper the word "Fredholm operator" refers to "Fredholm operator of index 0"). Weisstein, Eric W. "Fredholm's Theorem". MathWorld. B.V. Khvedelidze...

In mathematics, the Fredholm alternative, named after Ivar Fredholm, is one of Fredholm's theorems and is a result in Fredholm theory. It may be expressed...

selection theorem (mathematical analysis) Fredholm's theorem (linear algebra) Freidlin–Wentzell theorem (stochastic processes) Freiman's theorem (number...

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...

analysis included the construction of Fredholm determinants, and the proof of the Fredholm theorems. Fredholm was a member of the Finnish Society of...

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

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...

The Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear functionals defined on a vector subspace of...

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

In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...

In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result...

processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem (after Damodar Dharmananda...

In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It...

Stone's theorem on one-parameter unitary groups Holomorphic functional calculus Spectral theory Compact operator Laplace transform Fredholm theory Liouville–Neumann...

this statement is the Schwartz kernel theorem). The general theory of such integral equations is known as Fredholm theory. In this theory, the kernel is...

from Kuiper's theorem is the proof of the Atiyah–Jänich theorem (after Klaus Jänich and Michael Atiyah), stating that the space of Fredholm operators on...

In mathematics, Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician...

specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in...

relative point of view Grothendieck's theorem Grothendieck's theorem (Fredholm kernel) Grothendieck–Riemann–Roch theorem Grothendieck's Séminaire de géométrie...

{V}}y)(t)} can be described by the following uniqueness and existence theorem. Theorem — Let K ∈ C ( D ) {\displaystyle K\in C(D)} and let R {\displaystyle...

expected the proof of the Riemann Hypothesis would be a consequence of Fredholm's work on integral equations with a symmetric kernel. His collected works...

developed by Alexander Grothendieck while investigating the Schwartz kernel theorem and published in (Grothendieck 1955). We now describe this motivation....

multiplication theorem.[clarification needed] The next contributor of importance is Binet (1811, 1812), who formally stated the theorem relating to the...

convergence theorem Fatou's lemma Absolutely continuous Uniform absolute continuity Total variation Radon–Nikodym theorem Fubini's theorem Double integral...

stated above, the techniques used to prove results, e.g., the spectral theorem, in the non-compact case are typically different, involving operator-valued...

nevertheless strong enough for the Fredholm alternative, Schauder estimates, and the Atiyah–Singer index theorem. On the other hand, we need strong ellipticity...

by Karl Weierstrass to what is now known as the Lindemann–Weierstrass theorem. The transcendence of π implies that geometric constructions involving...

Theorem 12.6 Reed & Simon 1980, p. 38 Young 1988, p. 23. Clarkson 1936. Rudin 1987, Theorem 4.10 Dunford & Schwartz 1958, II.4.29 Rudin 1987, Theorem...