IEVref:103-01-03ID:
Language:enStatus: Standard
Term: distribution
Synonym1: generalized function
[Preferred]
Synonym2:
Synonym3:
Symbol:
Definition: 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@ .


Publication date:2009-12
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO
2017-08-25: Corrected </mtex> to </mtext>. LMO
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