I have an other question for a function different to the example given before in the link below: Exponential derivative operator and continuous functions We define for instance a function as: $$H(y)=\frac{1}{y^{-n}(d/dy)^{-n}e^{-(d/dy)y(d/dy)}T(y)}$$ where $T$ is not an operator but a function and $n$ is an integer. What can we say about the function and the operator? Is it possible to have $$H(y)=e^{(d/dy)y(d/dy)}(d/dy)^{n}y^{n}\frac{1}{T(y)}?$$