Maslov index in the infinite dimension and a splitting formula for a spectral flow

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抄録

First, we prove a local spectral flow formula (Theorem 3.7) for a differentiable curve of selfadjoint Fredholm operators. This formula enables us to prove in a simple way a general spectral flow formula (Theorem 3.$) which was already proved in [BF1]. Secondly, we prove a splitting formula (Theorem 4.12) for the spectral flow of a curve of selfadjoint elliptic operators on a closed manifold, which we decompose into two parts with commom boundary. Then the formula says that the spectral flow is a sum of two spectral flows on each part of the separated manifold with naturally introduced elliptic boundary conditions. In the course of proving this formula, we investigate a property of the Maslov index for paths of Fredholm pairs of Lagrangian subspaces.

収録刊行物

  • Japanese journal of mathematics. New series

    Japanese journal of mathematics. New series 28(2), 215-243, 2002-12-01

    一般社団法人 日本数学会

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各種コード

  • NII論文ID(NAID)
    10010086747
  • NII書誌ID(NCID)
    AA00690979
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    02892316
  • NDL 記事登録ID
    6403522
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z54-F36
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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