A Paley–Wiener theorem for Bergman spaces with application to invariant subspaces

Abstract

An analogue of the Paley-Wiener theorem is developed for weighted Bergman spaces of analytic functions in the upper half-plane. The result is applied to show that the invariant subspaces of the shift operator on the standard Bergman space of the unit disk can be identified with those of a convolution Volterra operator on the space L 2 (ℝ + ,(1/t)dt).