Does there exist a non constant entire function $f: \mathbb C \to \mathbb C$ which is square integrable i.e. $\int_{\mathbb C} \vert f(z)\vert^2 dz< \infty$ ?
I think that answer to above question is no and this should be direct application(probably by power series expansion of $f$) of some theorem but i am unable to solve this.Any ideas?