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Weighted generalization of the Szegö kernel and how it can be used to prove general theorems of complex analysis

  • Piotr Kielanowski
  • Anatol Odzijewicz
  • Emma Previato
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We consider weighted generalization of the Szegö kernel. We show which conditions must a weight of integration satisfy in order for weighted Szegö kernel to exist. Then we show some properties of weighted Szegö kernel, including a direct formula for particular cases. At the end, we show how weighted Szegö kernel can be used to prove general theorems of complex analysis.

Keywords

Reproducing kernel Hilbert space Szegö kernel. 

Mathematics Subject Classification (2000)

32A25 46E22. 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Piotr Kielanowski
    • 1
  • Anatol Odzijewicz
    • 2
  • Emma Previato
    • 3
  1. 1.Departamento de FísicaCINVESTAVCiudad de MéxicoMexico
  2. 2.Institute of MathematicsUniversity of BialystokBialystokPoland
  3. 3.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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