Meaning of this operator

Karlisbad

What's the meaning (if any) to this operator defined by the series:

[tex] \sum_{n=0}^{\infty} (-1)^{n}x^{n}\frac{d^{n}}{dx^{n}} [/tex]

i think i have seen this operator before, but i can't remember when or why. perhaps related to the "Theta" operator [tex] \Theta = x\frac{d}{dx} [/tex]