- #1
shoehorn
- 424
- 2
Suppose that we take the delta function [tex]\delta(x)[/tex] and a function f(x). We know that
[tex]\int_{-\infty}^{\infty} f(x)\delta(x-a)\,dx = f(a).[/tex]
However, does the following have any meaning?
[tex]\int_{-\infty}^{\infty} f(x)\delta(x-a)\delta(x-b)dx,[/tex]
for some constants [tex]-\infty<a,b<\infty[/tex].
[tex]\int_{-\infty}^{\infty} f(x)\delta(x-a)\,dx = f(a).[/tex]
However, does the following have any meaning?
[tex]\int_{-\infty}^{\infty} f(x)\delta(x-a)\delta(x-b)dx,[/tex]
for some constants [tex]-\infty<a,b<\infty[/tex].