Dirac Delta Function - Relationship To The Kronecker Delta

Relationship To The Kronecker Delta

The Kronecker delta is the quantity defined by

for all integers i, j. This function then satisfies the following analog of the sifting property: if is any doubly infinite sequence, then

Similarly, for any real or complex valued continuous function ƒ on R, the Dirac delta satisfies the sifting property

This exhibits the Kronecker delta function as a discrete analog of the Dirac delta function.