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A Direct Proof for an Eigenvalue Problem by Counting Lagrangian Submanifolds

  • Tomoyo KanazawaEmail author
Conference paper
  • 222 Downloads
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

  1. 1.Department of Mathematics Faculty of ScienceTokyo University of Science Kagurazaka 1-3, Shinjuku-ku162-8601Japan

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