Operational equations

Given an equation of the form K[f]=g for some functions f and g in a function space, when might we be able to recover the operator?

I think that one important special case that resolves down into theory of functions rather than in abstract functional analysis is the case of f, g in L^2 and K a bounded integral operator. If you impose enough conditions, just maybe you'll get a unique result! FUCK YEAH

0 is a bounded operator. Fuck off. You can recover that shit when K is invertible. Nobody gives a fuck about your faggoty L^p spaces.

Yeah, that's the goddamn question--WHEN THE FUCK IS K A BOUNDED INVERTIBLE OPERATOR, YOU DUMBSHIT FAGGOT

DEFINE THE FUNCTION SPACES FIRST YOU DUMBSHIT FAGGOT

This is a stupid fucking question. Why don't you just ask what operators don't have zero in their spectrum?

yeah fuck taht fuckity fucker fuck him fuck

Since when did math get so obscene? lol