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.

Read more about this topic:  Dirac Delta Function

Famous quotes containing the words representations of the, representations of and/or function:

    “These marbles, the works of the dreamers and idealists of old, live on, leading and pointing to good. They are the works of visionaries and dreamers, but they are realizations of soul, the representations of the ideal. They are grand, beautiful, and true, and they speak with a voice that echoes through the ages. Governments have changed; empires have fallen; nations have passed away; but these mute marbles remain—the oracles of time, the perfection of art.”
    —Herman Melville (1819–1891)

    “These marbles, the works of the dreamers and idealists of old, live on, leading and pointing to good. They are the works of visionaries and dreamers, but they are realizations of soul, the representations of the ideal. They are grand, beautiful, and true, and they speak with a voice that echoes through the ages. Governments have changed; empires have fallen; nations have passed away; but these mute marbles remain—the oracles of time, the perfection of art.”
    —Herman Melville (1819–1891)

    “Our father has an even more important function than modeling manhood for us. He is also the authority to let us relax the requirements of the masculine model: if our father accepts us, then that declares us masculine enough to join the company of men. We, in effect, have our diploma in masculinity and can go on to develop other skills.”
    —Frank Pittman (20th century)