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 Zhu [24] on Bargmann–Fock spaces. We also give a similar result on the union of two (or more) such zero sets, thereby establishing another conjecture of Shapiro [21] on Bergman spaces and allowing us to strengthen a result of Zhu [24] on Bargmann–Fock spaces.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
