PlanetMath: Dirac sequence

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Dirac sequence

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A Dirac sequence is a sequence $(\delta_k)$ of functions $\delta_k$ , which satisfies the following conditions:

$\delta_k\geq0$ for all .
$\int_{-\infty}^\infty\delta_k(t)dt=1$ for all .
For every and $\varepsilon>0$ there is an $N\in\mathbb{N}$ , such that for all we have
$\displaystyle \int_{\mathbb{R}\backslash[-r,r]}\delta_k(t)dt<\varepsilon.$

These functions “converge” to the Dirac delta function.

"Dirac sequence" is owned by mathwizard.

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Other names:

delta sequence

Attachments:: example of Dirac sequence (Example) by Johan
another example of Dirac sequence (Example) by Wkbj79

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Cross-references: Dirac delta function, functions, sequence
There are 3 references to this entry.

This is version 2 of Dirac sequence, born on 2004-02-25, modified 2006-12-08.
Object id is 5623, canonical name is DiracSequence.
Accessed 4210 times total.

Classification:

26A30 (Real functions :: Functions of one variable :: Singular functions, Cantor functions, functions with other special properties)

Pending Errata and Addenda

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