Delta Sequence

A delta sequence is a sequence of strongly peaked functions for which

(1)

for every smooth function of compact support. The limit is understood in the sense of generalized functions, and pointwise convergence is not required.

Examples include

			(2)
			(3)
			(4)
			(5)
			(6)
			(7)

(Arfken 1985, pp. 482 and 488-489).

A periodic analog is the normalized Dirichlet kernel

(8)

Its distributional limit is on . On the entire real line, the limit is the periodic impulse train , a rescaled Shah function.