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In mathematics, a '''Barnes integral''' or '''[[Hjalmar Mellin|Mellin]]– ...neralized hypergeometric function]]s _''p''''F''_''q'' in a similar way {{harv|Slater|1966}}. ...

...linear map between Fréchet spaces and wishes to show that it is surjective in order to use the open mapping theorem to deduce that it is also an open map ...\to X^{\prime}</math> will be [[injective]], but the converse is not true in general. ...

...] of an [[open set]] in a [[Euclidean space]]. Originally it was employed in the proof of [[Hassler Whitney]]'s [[Whitney extension theorem|extension th * {{cite book|last1=Grafakos|first1=Loukas|title=Classical Fourier Analysis|date=2008|publisher=Springer|isbn=978-0-387-09431-1}} ...

{{Short description|Theorem in functional analysis}} ...'s lemma''', named after [[Herman Auerbach]], is a theorem in [[functional analysis]] which asserts that a certain property of [[Euclidean space]]s holds for g ...

...sis of a [[function space]]. The result was originally proved by Stechkin in the case <math>q = 2</math>. ...math>N</math> largest terms of the sequence <math>(a_{i})_{i \in I}</math> in [[absolute value]]. Then ...

{{Short description|Theorem in mathematics about plurisubharmonic functions}} ...doconvex]]. Historically, this lemma was first shown in the Hartogs domain in the case of two variables. Furthermore, Oka's lemma is the inverse of Levi' ...

The '''Mackey–Arens theorem''' is an important theorem in [[functional analysis]] that characterizes those [[locally convex]] [[Topological vector space|ve ...ime} \in \mathcal{G}^{\prime}</math> then there exists a <math>G^{\prime} \in \mathcal{G}^{\prime}</math> such that <math>G_1^{\prime} \cup G_2^{\prime} ...

...'' (named after [[Frigyes Riesz]]) is an important theorem in [[functional analysis]] that states that a [[Hausdorff space|Hausdorff]] [[topological vector spa The theorem and its consequences are used ubiquitously in functional analysis, often used without being explicitly mentioned. ...

...hematics]], the '''Lions–Magenes lemma''' (or '''theorem''') is the result in the theory of [[Sobolev space]]s of [[Banach space]]-valued functions, whic ...0,T]</math> into <math>X</math>, and moreover the following equality holds in the sense of scalar [[distribution (mathematics)|distributions]] on <math>( ...

...the [[Stability theory|stability]] of delayed differential equations, and in particular, the stability of industrial processes with dead-time<ref>{{Cite <math display="block">\frac{d}{dt} v(t) \leq-\alpha v(t)+\beta\left[\sup _{s \in[t-\tau, t]} v(s)\right], t \geq t_{0} </math> ...

In [[number theory]], more specifically in [[p-adic analysis|''p''-adic analysis]], '''Krasner's lemma''' is a basic result relating the [[topological space ...{{overline|''K''}} be a [[separable closure]] of ''K''. Given an element α in {{overline|''K''}}, denote its [[Galois conjugate]]s by ''α''₂,& ...

...of of the [[Hardy–Littlewood maximal theorem]]. The lemma was a precursor in one dimension of the [[Calderón–Zygmund lemma]].<ref>{{harvnb|Stein|1998}}< ...(''x'',''b''] with ''g''(''y'') > ''g''(''x''). (Note that ''b'' cannot be in ''S'', though ''a'' may be.) Define ''E'' = ''S'' ∩ (''a'',''b''). ...

...hematics)|balls]] such that each point of ''E'' is the center of some ball in the cover. ...=&thinsp;{''B''_{''n''_{''c''_''N''}}} contained in '''F''' such that each collection ''A''_i consists of disjoint ba ...

...ionship between different methods of [[interpolation space|interpolation]] in [[Banach spaces]].<ref>{{cite journal |author=S. Kaijser |title=A New Proof ...Let <math>\bar{A} = (A_0, A_1)</math> be a Banach couple and let <math>a \in \Sigma(\bar{A})</math> be such that <math>\min(1,1/t)K(t,a) \to 0</math> wh ...

...] and volume computation via [[random walks]]; finding edge disjoint paths in [[expander graphs]], and exploring [[anti-Ramsey theory]] and the stability ...e of a membership oracle. The algorithm takes time bounded by a polynomial in <math>n</math>, the dimension of <math>K</math> and <math>1/\epsilon</math> ...

{{Short description|Type of graph in mathematics}} In [[graph theory]], a branch of [[mathematics]], a '''half graph''' is a spec ...

{{Short description|Optimization algorithm in computer science}} ...c''. It heuristically packs numbers into bins such that the sum of numbers in each bin is at most ''C'', aiming to use as few bins as possible. Multifit ...

...o Kakutani]]. The lemma is used extensively in ergodic theory, for example in [[Ornstein isomorphism theorem|Ornstein theory]] and has many generalizatio ...is which are traditionally called lemmas despite the fact that their roles in their respective fields are fundamental. ...

In mathematics, '''Watson's lemma''', proved by [[G. N. Watson]] (1918, p. 133 ...(t)</math>, where <math>g(t)</math> has an infinite number of derivatives in the neighborhood of <math>t=0</math>, with <math>g(0)\neq 0</math>, and <ma ...

{{Short description|Method in combinatorics}} ...], and [[Ramsey theory]]; they include some of the most classical problems in the associated fields. ...