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.

Read more about this topic:  Dirac Delta Function

Famous quotes containing the words relationship to and/or relationship:

    Women, because of their colonial relationship to men, have to fight for their own independence. This fight for our own independence will lead to the growth and development of the revolutionary movement in this country. Only the independent woman can be truly effective in the larger revolutionary struggle.
    Women’s Liberation Workshop, Students for a Democratic Society, Radical political/social activist organization. “Liberation of Women,” in New Left Notes (July 10, 1967)

    Living in cities is an art, and we need the vocabulary of art, of style, to describe the peculiar relationship between man and material that exists in the continual creative play of urban living. The city as we imagine it, then, soft city of illusion, myth, aspiration, and nightmare, is as real, maybe more real, than the hard city one can locate on maps in statistics, in monographs on urban sociology and demography and architecture.
    Jonathan Raban (b. 1942)