Dirac Delta Function - Representations of The Delta Function

Representations of The Delta Function

The delta function can be viewed as the limit of a sequence of functions

where ηε(x) is sometimes called a nascent delta function. This limit is meant in a weak sense: either that

(5)

for all continuous functions ƒ having compact support, or that this limit holds for all smooth functions ƒ with compact support. The difference between these two slightly different modes of weak convergence is often subtle: the former is convergence in the vague topology of measures, and the latter is convergence in the sense of distributions.

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