TY - JOUR

T1 - On the number of zeros of functions in analytic quasianalytic classes

AU - Sodin, Sasha

N1 - Publisher Copyright:
© Sasha Sodin, 2020.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Analytic quasianalyticity

KW - Number of zeros

KW - Quasianalytic class

UR - http://www.scopus.com/inward/record.url?scp=85086017517&partnerID=8YFLogxK

U2 - 10.15407/mag16.01.055

DO - 10.15407/mag16.01.055

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AN - SCOPUS:85086017517

SN - 1812-9471

VL - 16

SP - 55

EP - 65

JO - Journal of Mathematical Physics, Analysis, Geometry

JF - Journal of Mathematical Physics, Analysis, Geometry

IS - 1

ER -