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

By Peter L. Duren, Eva A. Gallardo-Gutiérrez, A. Montes-Rodríguez. 2007

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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 L2(ℝ+, (1/t)dt).

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bb3a131a079633146d82196d14dd64abad95556d