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==Values in Banach spaces== For a function ''f'' with values in a [[Banach space]] (or [[Fréchet space]]), ''strong me ...

...a}</math> is a space of [[test function]]s for the theory of [[generalized function]]s, introduced by {{harvs|txt|last=Gelfand|author1-link=Israel Gelfand|last ...eong|last3=Kim|first3=Dohan|title=Characterizations of the Gel'fand–Shilov spaces via Fourier transforms|doi=10.1090/S0002-9939-96-03291-1|mr=1322917|year=19 ...

...cepts are different. The relationship between the sub-Stonean spaces and F-spaces is studied in Henriksen and Woods, 1989. ...orona set]]s of locally compact σ-compact Hausdorff spaces are sub-Stonean spaces. ...

Let <math>(X_i)_{i \in I}</math> be a family of Banach spaces, where <math>I</math> may have arbitrarily large cardinality. Set ...\mu</math>), and each element <math>(x_i)_{i \in I} \in P</math> induces a function ...

{{Short description|Generalization of Sobolev spaces}} ...defined [[Triebel–Lizorkin space]]s, serve to generalize more elementary [[function space]]s such as [[Sobolev space]]s and are effective at measuring regulari ...

...ns with regard to their local and global behavior. While the concept of [[function space]]s treating local and global behavior separately was already known ea ...\|\cdot \|_X </math>. Then the ''Wiener amalgam space''<ref>Wiener amalgam spaces for the Fundamental Identity of Gabor Analysis by Hans Georg Feichtinger an ...

...graph theorem]] is valid for [[linear map]]s defined on and valued in most spaces encountered in analysis.{{sfn|Trèves|2006|p=549}} ...an space]] as well as many other spaces that occur in analysis are Souslin spaces. The Borel graph theorem states:{{sfn|Trèves|2006|p=549}} ...

...results about isomorphic measurable spaces, see [[Borel set#Standard Borel spaces and Kuratowski theorems|Kuratowski's theorem]]. However, (a) the latter the Let <math>X</math> and <math>Y</math> be measurable spaces. If there exist injective, bimeasurable maps <math>f : X \to Y, </math> <ma ...

...[Polish space]]. Except in the case of [[discrete space|discrete]] Polish spaces, the standard Borel space is unique, up to [[isomorphism]] of [[measurable ...ces have several useful properties that do not hold for general measurable spaces. ...

...in [[metric space]] that contains all [[separable space|separable]] metric spaces in a particularly nice manner. This [[mathematics]] concept is due to [[Pav ...''Urysohn universal''<ref>{{citation|title=Geometric embeddings of metric spaces|url=http://www.math.jyu.fi/research/reports/rep90.ps|author=Juha Heinonen|d ...

...ded mean oscillation]], describing situations where the oscillation of the function in a ball is proportional to some power of the [[radius]] other than the di The [[seminorm]] of the Morrey spaces is given by ...

...f><ref>{{cite web|last=Strickland|first=Neil P.|title=The category of CGWH spaces|year=2009|url=http://neil-strickland.staff.shef.ac.uk/courses/homotopy/cgwh ...logy]]. For that, see the [[category of compactly generated weak Hausdorff spaces]]. ...

...' (born 1968){{r|ros}} is a German mathematician who holds the chair for [[function space]]s in the Institute of Mathematics of the [[University of Jena]].{{r| ...ctoral dissertation, ''Entropy Numbers and Application Numbers in Weighted Function Space of Type <math>B^s_{pq}</math> and <math>F^s_{pq}</math>, Eigenvalue D ...

...86(2):307–340, 1989.</ref><ref>H. G. Feichtinger and K. Gröchenig. "Banach spaces related to integrable group representations and their atomic decompositions ...pace]] <math>\mathcal H</math>, with which one can define a transform of a function <math>f \in \mathcal H</math> with respect to <math>g\in \mathcal H</math> ...

| title = Maximally decomposable spaces ....|last2=Tironi|first2=G|year=2000|title=Weakly Fréchet–Urysohn and Pytkeev spaces|journal=Topology and Its Applications|volume=104|issue=2|pages=181–190|doi= ...

In [[mathematics]], certain [[Function (mathematics)|functions]] useful in [[functional analysis]] are called '''Y ...ction <math>x \mapsto 0</math> , and it is not the convex dual of the zero function <math>x \mapsto \begin{cases} 0 \text{ if } x = 0, \\ +\infty \text{ else.} ...

...or Tzafriri, ''Classical Banach Spaces I and II: Sequence Spaces; Function Spaces'', Springer 1996, {{ISBN|3540606289}}, p. 16. * Przemysław Wojtaszczyk, ''Banach spaces for analysts''. Cambridge Studies in Advancod Mathematics, Cambridge Univer ...

...ort description|Endofunctor on the category V of finite-dimensional vector spaces}} ...of finite-dimensional vector spaces]] that depends polynomially on vector spaces. For example, the [[symmetric power]]s <math>V \mapsto \operatorname{Sym}^n ...

...th [[continuous function]]s for morphisms to the [[category of topological spaces]]. If <math>d_1</math> and <math>d_2</math> are [[equivalent metrics]] on a ...

...zed families of vector spaces to smoothly parameterized families of vector spaces. Smooth functors may therefore be uniquely extended to functors defined on ...ant functor|covariant]] functor that maps '''Vect''' to itself. For vector spaces ''T'', ''U'' ∈ '''Vect''', the functor ''F'' induces a mapping ...