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Dirac Delta Functions Via Nonstandard Analysis
Published online by Cambridge University Press: 20 November 2018
Extract
We recall that a Dirac delta function δ(x) in the real number system is the idealization of a function that vanishes outside a "short" interval and satisfies
It is conceived as a function δ for which δ(0)=+ ∞, δ(t)=0 if t≠0, and
This function should possess the "sifting property"
for any continuous function f. Even though certain sequences of functions are used, via a limit operation, to approximate a Dirac delta function (for details, see [3] and [4]), no function in
has these properties.
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- Copyright © Canadian Mathematical Society 1975
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