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Collectanea Mathematica

, Volume 68, Issue 2, pp 251–263 | Cite as

De Branges functions of Schroedinger equations

  • A. Baranov
  • Y. Belov
  • A. Poltoratski
Article
  • 132 Downloads

Abstract

We characterize the Hermite–Biehler (de Branges) functions E which correspond to Schroedinger operators with \(L^2\) potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also obtain a result about location of resonances.

Keywords

Entire Function Dirichlet Boundary Condition Exponential Type Canonical System Characterization Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors are grateful to the referee for numerous helpful remarks and, especially, for suggesting a simplified proof of Statement 1 in Theorem 3.

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Copyright information

© Universitat de Barcelona 2016

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Chebyshev LaboratorySt. Petersburg State UniversitySt. PetersburgRussia
  3. 3.Department of MathematicsTexas A&M UniversityCollege StationUSA

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