On the number of zeros of functions in analytic quasianalytic classes

Sasha Sodin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A space of analytic functions in the unit disc with uniformly continuous derivatives is said to be quasianalytic if the boundary value of a non-zero function from the class can not have a zero of infinite multiplicity. Such classes were described in the 1950-s and 1960-s by Carleson, RodriguesSalinas and Korenblum. A non-zero function from a quasianalytic space of analytic functions can only have a finite number of zeros in the closed disc. Recently, Borichev, Frank, and Volberg proved an explicit estimate on the number of zeros for the case of quasianalytic Gevrey classes. Here, an estimate of similar form for general analytic quasianalytic classes is proved using a reduction to the classical quasianalyticity problem.

Original languageEnglish
Pages (from-to)55-65
Number of pages11
JournalJournal of Mathematical Physics, Analysis, Geometry
Issue number1
StatePublished - 2020


FundersFunder number
Horizon 2020 Framework Programme639305
Royal Society
European Research Council


    • Analytic quasianalyticity
    • Number of zeros
    • Quasianalytic class


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