Distribution (mathematics)
label: Teoría de distribuciones @es
label: Teoria dystrybucji @pl
label: توزيع (رياضيات) @ar
label: Teoria das distribuições @pt
label: Distribuzione (matematica) @it
label: Обобщённая функция @ru
label: 분포 (해석학) @ko
label: 分布 (数学分析) @zh
label: Distribution @sv
label: Distribucio @eo
label: Distributie (wiskunde) @nl
label: Узагальнена функція @uk
label: Distribuce (matematika) @cs
label: Distribution (mathématiques) @fr
label: シュワルツ超函数 @ja
label: Distribution (Mathematik) @de
label: Distribució (matemàtiques) @ca
subject: Category:Articles containing proofs
subject: Category:Linear functionals
subject: Category:Generalized functions
subject: Category:Functional analysis
subject: Category:Generalizations of the derivative
subject: Category:Differential equations
subject: Category:Smooth functions
subject: Category:Schwartz distributions
author link: Sergei Lvovich Sobolev
author link: Vasilii Sergeevich Vladimirov
id: G/g130030
id: G/g043820
id: G/g043840
id: G/g043810
id: G/g043830
text: The vector space is endowed with the locally convex topology induced by any one of the four families of seminorms described above. This topology is also equal to the vector topology induced by of the seminorms in
text: Definition: Elements of are called ' on and is called the ' on . We will use both and to denote this space.
text: By definition, a is a continuous linear functional on Said differently, a distribution on is an element of the continuous dual space of when is endowed with its canonical LF topology.
text: Suppose and is an arbitrary compact subset of Suppose is an integer such that and is a multi-index with length For and define: while for define all the functions above to be the constant map.
text: is called the and it may also be denoted by Unless indicated otherwise, it is endowed with a topology called , whose definition is given in the article: Spaces of test functions and distributions.
text: Assumption: For any compact subset we will henceforth assume that is endowed with the subspace topology it inherits from the Fréchet space
left: true
name: Theorem
name: Theorem.
name: Lemma
name: Corollary
description: mathematischer Begriff @de
description: دالة رياضية @ar
description: kontinua funkcionalo sur spaco de testfunkcioj, kiu ĝeneraligas la koncepton de loke integrebla funkcio @eo
description: un funcional lineal sobre el espacio de funciones infinitamente diferenciables y compactamente soportadas @es
description: פונקציונל רציף על מרחב של פונקציות מבחן (מרחב שוורץ), שמכליל את מושג הפונקציות האינטגרביליות באופן מקומי @iw
description: неперервний функціонал на просторі пробних функцій (простір Шварца), що узагальнює поняття локально інтегровних функцій @uk
description: un objet qui généralise la notion de fonction et de mesure @fr
description: функцыя @be
description: dział matematyki @pl
description: istilah analisis matematik @ms
description: funcțional continuu pe spațiul Schwartz @ro
description: テスト関数空間上の連続汎関数 @ja
description: a continuous functional on a space of test functions (Schwartz space), which generalizes the concept of locally integrable functions
description: функция для статистических величин @ru
description: matematikai fogalom @hu
description: wiskunde @nl
description: mga bagay na binibigyan ng tuntuning panlahat ang klasikal na paniniwala ng punsyon sa pagsusuring pangmatematika @tl
wiki page external link: http://mi.mathnet.ru/msb5358
wiki page external link: https://archive.org/details/introductiontofo0000stei
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Integration_by_parts
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Engineering
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Banach_space
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Category:Generalized_functions
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Pullback_(differential_geometry)
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Hermitian_adjoint
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Continuous_linear_operator
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Holomorphic_function
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Quantum_field_theory
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Submersion_(mathematics)
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Transpose
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Transpose_of_a_linear_map
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Minkowski_sum
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Heaviside_step_function
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Functional_analysis
wiki page wiki link: https://dbpedia-live.demo.openlinksw.com/resource/Bump_function