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Dirac sequence

A Dirac sequence is a sequence $(\delta_{k})$ of functions $\delta_{k}$ , which satisfies the following conditions:

1.

$\delta_{k}\geq 0$ for all $k$ .
2.

$\int_{-\infty}^{\infty}\delta_{k}(t)dt=1$ for all $k$ .

3.

For every $r>0$ and $\varepsilon>0$ there is an $N\in\mathbb{N}$ , such that for all $k>N$ we have

$\int_{\mathbb{R}\backslash[-r,r]}\delta_{k}(t)dt<\varepsilon.$

These functions “converge” to the Dirac delta function.

Title	Dirac sequence
Canonical name	DiracSequence
Date of creation	2013-03-22 14:11:35
Last modified on	2013-03-22 14:11:35
Owner	mathwizard (128)
Last modified by	mathwizard (128)
Numerical id	5
Author	mathwizard (128)
Entry type	Definition
Classification	msc 26A30
Synonym	delta sequence
Related topic	DiracDeltaFunction
Related topic	FejerKernel