I was reading the wikipedia page on Differential Operators..
It introduces the general concept of a differential operator and then it goes through some examples.
It mentions the derivative, the theta operator, the laplacian, the del operator, what is an adjoint of a linear operator, etc..
I'd like to know if there are some books,resources where these topics are treated in a general, related way.
I had the exactly the same problem for years. I thought this must be a secret (my teachers never tell where they learned from) until I read a series paper by Achim Kempf.
The introductory start can be Shift Operator and Operational Calculus.
Bunch of good resources referenced in Wiki pages.
H. Jeffreys (1927) Operational Methods In Mathematical Physics
Marchenko, V. A. (2006). "The generalized shift, transformation operators, and inverse problems"
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