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...
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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...
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In this paper the word "Fredholm operator" refers to "Fredholm operator of index 0"). Weisstein, Eric W. "Fredholm's Theorem". MathWorld. B.V. Khvedelidze...
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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...
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selection theorem (mathematical analysis) Fredholm's theorem (linear algebra) Freidlin–Wentzell theorem (stochastic processes) Freiman's theorem (number...
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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...
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analysis included the construction of Fredholm determinants, and the proof of the Fredholm theorems. Fredholm was a member of the Finnish Society of...
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geometry Fredholm number, in number theory, apparently not in fact studied by Fredholm Fredholm operator, in mathematics Fredholm's theorem, in mathematics...
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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...
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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...
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In operator theory, Atkinson's theorem (named for Frederick Valentine Atkinson) gives a characterization of Fredholm operators. Let H be a Hilbert space...
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In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...
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In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result...
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processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem (after Damodar Dharmananda...
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In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It...
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Resolvent formalism (category Fredholm theory)
Stone's theorem on one-parameter unitary groups Holomorphic functional calculus Spectral theory Compact operator Laplace transform Fredholm theory Liouville–Neumann...
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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...
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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...
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Farkas' lemma (redirect from Theorem of alternatives)
In mathematics, Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician...
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specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in...
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relative point of view Grothendieck's theorem Grothendieck's theorem (Fredholm kernel) Grothendieck–Riemann–Roch theorem Grothendieck's Séminaire de géométrie...
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{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...
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David Hilbert (section Theorems)
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...
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Nuclear space (redirect from Bochner-Minlos theorem)
developed by Alexander Grothendieck while investigating the Schwartz kernel theorem and published in (Grothendieck 1955). We now describe this motivation....
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Determinant (redirect from Determinant theorem)
multiplication theorem.[clarification needed] The next contributor of importance is Binet (1811, 1812), who formally stated the theorem relating to the...
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convergence theorem Fatou's lemma Absolutely continuous Uniform absolute continuity Total variation Radon–Nikodym theorem Fubini's theorem Double integral...
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stated above, the techniques used to prove results, e.g., the spectral theorem, in the non-compact case are typically different, involving operator-valued...
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Elliptic operator (section Elliptic regularity theorem)
nevertheless strong enough for the Fredholm alternative, Schauder estimates, and the Atiyah–Singer index theorem. On the other hand, we need strong ellipticity...
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Transcendental number (redirect from Fredholm number)
by Karl Weierstrass to what is now known as the Lindemann–Weierstrass theorem. The transcendence of π implies that geometric constructions involving...
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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...
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