Zero Sets for Spaces of Analytic Functions

ANNALES DE L INSTITUT FOURIER, pp. 2311-2328, 2018.

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Abstract:

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann- Fock space has the property that a.s. no non-zero function in that space vanishes where F does. This establishes a conjecture of Shapiro [21] on Bergman spaces and allows us to resolve a question of Z...More

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