I think I may be missing something...so whenever we write L= (...) + (...) + (...), is L necessarily always a LINEAR operator? Can nonlinear 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) ?
