>>10929346It's a function on functions, i.e. it eats a function and gives back a number. Every function gives a distribution defined by
Dirac's delta is a distribution defined by . This distribution doesn't arise as an integral against a function, I mean there is no function such that . But IF THERE WAS, it would have to satisfy
for any (smooth and compactly supported) function . In particular, you would get that is zero everywhere except the origin, but its integral over any interval containing the origin gives 1. So if it existed, it would need to look like pic related. But that's just an intuition, no such function exists.
