I have an other question for a function different to the example given before in the link below:
https://mathoverflow.net/questions/405078/exponential-derivative-operator-and-continuous-functions/405092#405092
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?
$$H(y)=e^{(d/dy)y(d/dy)}(d/dy)^{n}y^{n}\frac{1}{T(y)}$$