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...of maps is a point that is [[Fixed point (mathematics)|fixed]] by each map in the set.) ...sed on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit.<ref>{{cite journal|first=C.|last=Ryll-Nardzewski|title ...

...ing of <math>K</math> into itself such that <math>f(K)</math> is contained in a [[compact set|compact]] subset of <math>K</math>, then <math>f</math> has Schaefer's theorem is in fact a special case of the far reaching [[Leray–Schauder theorem]] which wa ...

...[[Osaka University|Osaka]] and [[Nagoya University|Nagoya Universities]]. In 1955, Yosida returned to the University of Tokyo. * [[Functional analysis]] ...

...stated in terms of integral equations, in terms of [[linear algebra]], or in terms of the [[Fredholm operator]] on [[Banach space]]s. The [[Fredholm alternative]] is one of the Fredholm theorems. ...

{{short description|One of several theorems in different areas of mathematics}} ...theorem''' is a theorem of [[:de:Axel Schur|Axel Schur]]. In [[functional analysis]], '''Schur's theorem''' is often called [[Schur's property]], also due to ...

This is a '''list of [[functional analysis]] topics'''. See also: [[Glossary of functional analysis]]. ...

In [[functional analysis]], a branch of [[mathematics]], the '''Hellinger–Toeplitz theorem''' states for all ''x'', ''y'' in the domain of ''A''. Note that symmetric ''everywhere-defined'' operators ...

{{Short description|Mathematical method in functional analysis}} In [[functional analysis]], it is often convenient to define a [[linear transformation]] on a [[Comp ...

...graph theorem in [[functional analysis]]|Closed graph theorem (functional analysis)}} ...er to one of several basic results characterizing [[continuous function]]s in terms of their [[graph of a function|graph]]s. ...

...s called the '''Moser–Trudinger inequality''') is a result of [[functional analysis]] on [[Sobolev space]]s. It is named after [[Neil Trudinger]] (and [[Jürgen Let <math>\Omega</math> be a bounded domain in <math>\mathbb{R}^n</math> satisfying the [[cone condition]]. Let <math>mp=n ...

* [[Abelian group]], a group in which the binary operation is commutative * [[Abelian category]], in category theory, a preabelian category in which every monomorphism is a kernel and every epimorphism is a cokernel ...

In [[mathematics]], a '''representation theorem''' is a [[theorem]] that state *: Another variant, [[Stone's duality]], states that there exists a duality (in the sense of an arrow-reversing equivalence) between the [[category (mathem ...

{{short description|Mathematical theorem related to real and functional analysis}} In [[mathematics]], specifically [[real analysis]] and [[functional analysis]], the '''Kirszbraun theorem''' states that if {{mvar|U}} is a [[subset]] o ...

* [[Analysis of Boolean functions]] [[Talk:Analysis of Boolean functions| ]] * [[Functional completeness]] [[Talk:Functional completeness| ]] ...

{{About|Bochner's theorem in [[harmonic analysis]]|Bochner's theorem in Riemannian geometry|Bochner's theorem (Riemannian geometry)}} ...ve finite [[Borel measure]] on the real line. More generally in [[harmonic analysis]], Bochner's theorem asserts that under Fourier transform a continuous [[Po ...

==Theorems of which articles are primarily devoted to proving them== ==Articles devoted to theorems of which a (sketch of a) proof is given== ...

...century which aimed to abolish all geometric intuition from the proofs in analysis. For the followers of this program, the fundamental concepts of calculus sh ...''arithmetization of analysis'', by which he meant its constructivization in the context of the [[natural number]]s (see quotation at bottom of page). ...

{{Short description|Theorem in harmonic analysis}} ...el]] in 1910. It is a generalization of [[Parseval's theorem]]; often used in the fields of science and engineering, proving the [[unitary transformation ...

...eraction|forces of nature]] are believed to have their natural description in terms of [[Field (physics)#Quantum fields|quantum fields]]. ...xioms|operator-valued distribution]], a type of object from [[mathematical analysis]]. The [[existence theorem]]s for quantum fields can be expected to be ver ...

...al results factored out of proofs). See also [[list of axioms]], [[list of theorems]] and [[list of conjectures]]. {{Main category|Lemmas in algebra}} ...