Find a polynomial $P\_{n}\in{\mathbb{C}[X]}$ such as $S\_{n}=\ker P\_{n}(D)$

-With $S\_{n}$ $(n\geq 1)$ all of the functions such as $y^{(n)}=y $  

(where $y^{(n)}$ is the nth derivative of $y$)

-D the endomorphism sending the functions $C^{\infty}$ on their derivatives D : y -> y'

I already proved that D is an endomorphism and $S\_{n}$ a vector space containing the functions $ke^x$

But my probleme is that i dont really understand the meaning of $P\_{n}(D)$, and so dont see what $S\_{n}=ker P\_{n}(D)$ could be. It probably have to do with eigenvalues, eigenvectors...But really I dont see anything.

Thanks for your help