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Area Mathematics - Functions / General concepts

IEV ref103-01-03

en
distribution
generalized function
continuous linear functional which assigns a real or complex number to any function of a real or complex variable belonging to the class of infinitely differentiable functions vanishing outside a bounded interval or domain

Note 1 to entry: A function D(x) can be considered as a distribution D assigning to a function f(x) the value

D(f)= + D(x)f(x)dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaaiaadseacaGGOaGaam OzaiaacMcacqGH9aqpdaWdXbqaaiaadseacaGGOaGaamiEaiaacMca caWGMbGaaiikaiaadIhacaGGPaqcLbqacaGGKbGccaWG4baaleaacq GHsislcqGHEisPaeaacqGHRaWkcqGHEisPa0Gaey4kIipaaaa@4939@ if this integral exists.

Note 2 to entry: The derivative of a distribution D is another distribution D′ defined for any function f(x) by

D (f)=D(df/dx) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaaiqadseagaqbaiaacI cacaWGMbGaaiykaiabg2da9iabgkHiTiaadseacaGGOaqcLbqacaGG KbGccaWGMbGaai4laiaayIW7jugabiaacsgakiaadIhacaGGPaaaaa@436A@ .


fr
distribution, f
fonction généralisée, f
fonctionnelle linéaire continue qui associe un nombre réel ou complexe à toute fonction de variable réelle ou complexe appartenant à la classe des fonctions indéfiniment dérivables nulles en dehors d'un intervalle ou domaine borné

Note 1 à l'article: Une fonction D(x) peut être considérée comme une distribution D associant à une fonction f(x) la valeur

D(f)= + D(x)f(x)dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaaiaadseacaGGOaGaam OzaiaacMcacqGH9aqpdaWdXbqaaiaadseacaGGOaGaamiEaiaacMca caWGMbGaaiikaiaadIhacaGGPaqcLbqacaGGKbGccaWG4baaleaacq GHsislcqGHEisPaeaacqGHRaWkcqGHEisPa0Gaey4kIipaaaa@4939@ si cette intégrale existe.

Note 1 à l'article: 2 La dérivée d'une distribution D est une autre distribution D′ définie pour toute fonction f(x) par

D (f)=D(df/dx) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaaiqadseagaqbaiaacI cacaWGMbGaaiykaiabg2da9iabgkHiTiaadseacaGGOaqcLbqacaGG KbGccaWGMbGaai4laiaayIW7jugabiaacsgakiaadIhacaGGPaaaaa@436A@ .


ar
توزيع
دالة تعميمية

de
Distribution, f
verallgemeinerte Funktion, f

es
distribución

it
distribuzione
funzione generalizzata

ja
分布
一般関数

pl
dystrybucja
funkcja uogólniona

pt
distribuição
função generalizada

sr
дистрибуција, ж јд
генерализована функција, ж јд

sv
distribution
generaliserad funktion

zh
分布
广义函数

Publication date: 2009-12
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