See for impulse response vs Greens function
https://physics.stackexchange.com/q/363845/45664
but no answer was given although there were many good comments.
See for Greens function vs fundamental solution
https://physics.stackexchange.com/q/377683/45664
but again no answer was given although there were many good comments.
Also see
Difference between the fundamental solution and the Green function
where an (the?) accepted answer is given for fundamental solution vs greens function.
Then see L. Schwartz,"Mathematics for the Physical Sciences" p.281 where for operator L the elementary solution, E, is essentially defined as $L(E)=\delta$
and I. M. Gelfand, "Generalized Functions" p. 107, where the elementary solution is again essentially defined as $L(E)=\delta$
also https://en.wikipedia.org/wiki/Fundamental_solution where the fundamental solution is given as $L(F)=\delta(x)$
Finally, I remember seeing somewhere that the impulse response of L is given as $L(I)=\delta$
My question is: What is the difference between the impulse response, Green's function, fundamental solution and elementary solution?
If no differences, why so many names for the same thing?
Note that in all cases the equation with the operator is non homogeneous. A forcing function, $\delta$, is required.
See for almost the same question but with additional different functions (except for Green function):
https://physics.stackexchange.com/q/20797/45664
See also:
