Is is possible to talk about a "space of differential operators"? If one defined such a space would it be possible to talk about limits? I don't really have much background so I'm really just looking for a simple/intuitive explanation?
For example if there was a space of differential operators, and it was normed could I then find limits? If you were to take the sum of two differential operators would you get a new differential operator in that space? I'm sure all these questions have answers I just don't know where to find a good introduction to some of these ideas.