Beurling's phenomenon on analytic Hilbert spaces over the complex plane.

In this paper, we show that Beurling's theorem on analytic Hilbert spaces over the complex plane analogous to the Hardy space or the Bergman space does not hold, but for finite co-dimensional quasi-invariant subspaces, they are generated by their wandering subspace if and only if they are generated by $z^n$ provided that the order of the reproducing kernels $K_lambda (z)$ is less than 2 but not equal to 1. [ABSTRACT FROM AUTHOR]