I think I may be missing something...so whenever we write L= (...) + (...) + (...), is L necessarily always a LINEAR operator? Can non-linear operators be expressed this way?
Also, there is something in general that I don't understand about operators...(I'm just guessing that I can do things like the following)
If L=∂xy + cos(x) + (∂y)2, to find Lu, should we just imagine multiplying L with u (just like multiplying real numbers?), so
Lu = [∂xy + cos(x) + (∂y)2] u
=∂xy u + cos(x) u + (∂y)2 u (by distributive law of multiplication) ?