On the number of zeros of functions in analytic quasianalytic classes
| Autor: | Sasha Sodin |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Complex Variables
Mathematics::Complex Variables 010102 general mathematics Mathematics::Classical Analysis and ODEs 0102 computer and information sciences 01 natural sciences Mathematics - Classical Analysis and ODEs 010201 computation theory & mathematics Classical Analysis and ODEs (math.CA) FOS: Mathematics Geometry and Topology 0101 mathematics Complex Variables (math.CV) Mathematical Physics Analysis Mathematics |
| Zdroj: | Zurnal matematiceskoj fiziki, analiza, geometrii |
| DOI: | 10.48550/arxiv.1902.05016 |
| Popis: | 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, Rodrigues-Salinas 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. Comment: v1: 9pp. v2: 10pp, fixed typos, added comments and ref-s. v3: fixed a few more typos. v4: fixed two more typos. To appear in "Journal of Mathematical Physics, Analysis, Geometry" |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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