Localization of Zeros in Cauchy–de Branges Spaces

  • Evgeny AbakumovEmail author
  • Anton Baranov
  • Yurii Belov
Part of the Trends in Mathematics book series (TM)


We study the class of discrete measures in the complex plane with the following property: up to a finite number, all zeros of any Cauchy transform of the measure (with 2-data) are localized near the support of the measure. We find several equivalent forms of this property and prove that the parts of the support attracting zeros of Cauchy transforms are ordered by inclusion modulo finite sets.


Cauchy transforms de Branges spaces Distribution of zeros of entire functions Polynomial approximation 

1991 Mathematics Subject Classification

30D10 30D15 46E22 41A30 34B20 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University Paris-Est, LAMA (UMR 8050), UPEM, UPEC, CNRS,Marne-la-ValléeFrance
  2. 2.Department of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  3. 3.National Research University Higher School of EconomicsSt. PetersburgRussia
  4. 4.St. Petersburg State UniversitySt. PetersburgRussia

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