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A Direct Proof for an Eigenvalue Problem by Counting Lagrangian Submanifolds

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

Abstract

We focus on one of the Schrödinger operators called the Bochner– Laplacian. Using Jensen’s Formula and Vandermonde convolution, we show directly that for each k = 0, 1, 2, . . . , the number of Lagrangian submanifolds which satisfy the Maslov quantization condition is just equal to the multiplicity of the kth eigenvalue of the operator.

Keywords

Jensen’s Formula Vandermonde convolution Bochner-Laplacian. 

Mathematics Subject Classification (2000)

Primary 05A10 Secondary 53D12. 

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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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