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

1.
${\delta}_{k}\ge 0$ for all $k$.

2.
${\int}_{\mathrm{\infty}}^{\mathrm{\infty}}{\delta}_{k}(t)\mathit{d}t=1$ for all $k$.

3.
For every $r>0$ and $\epsilon >0$ there is an $N\in \mathbb{N}$, such that for all $k>N$ we have
$$
These functions “converge” to the Dirac delta function.
Title  Dirac sequence 

Canonical name  DiracSequence 
Date of creation  20130322 14:11:35 
Last modified on  20130322 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 