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Algebraic Analysis of Differential Equations

from Microlocal Analysis to Exponential Asymptotics

  • Book
  • © 2008

Overview

Editors:
  1. Takashi Aoki

    1. Department of Mathematics, Kinki University, Higashi-Osaka, Japan

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  2. Hideyuki Majima

    1. Department of Mathematics, Ochanomizu University, Tokyo, Japan

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  3. Yoshitsugu Takei

    1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

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  4. Nobuyuki Tose

    1. Faculty of Economics, Keio University, Yokohama, Japan

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Table of contents (27 chapters)

  1. Front Matter

    Pages I-XVII
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  3. Contributed papers

    1. Front Matter

      Pages 27-27
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    2. Virtual turning points — A gift of microlocal analysis to the exact WKB analysis

      • Takashi Aoki, Naofumi Honda, Takahiro Kawai, Tatsuya Koike, Yukihiro Nishikawa, Shunsuke Sasaki et al.
      Pages 29-43

    3. Regular sequences associated with the Noumi-Yamada equations with a large parameter

      • Takashi Aoki, Naofumi Honda
      Pages 45-53

    4. Ghost busting: Making sense of non-Hermitian Hamiltonians

      • Carl M. Bender
      Pages 55-66

    5. Vanishing of the logarithmic trace of generalized Szegö projectors

      • Louis Boutet de Monvel
      Pages 67-78

    6. Nonlinear Stokes phenomena in first or second order differential equations

      • Ovidiu Costin
      Pages 79-87

    7. Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation

      • Yuki Daido, Hyeonbae Kang, Gen Nakamura
      Pages 89-99

    8. Exact WKB analysis near a simple turning point

      • Eric Delabaere
      Pages 101-117

    9. The Borel transform

      • Leon Ehrenpreis
      Pages 119-131

    10. On the use of Z-transforms in the summation of transseries for partial differential equations

      • Christopher J. Howls
      Pages 133-141

    11. Some dynamical aspects of Painlevé VI

      • Katsunori Iwasaki
      Pages 143-156

    12. An algebraic representation for correlation functions in integrable spin chains

      • Michio Jimbo
      Pages 157-166

    13. Inverse image of D-modules and quasi-b-functions

      • Yves Laurent
      Pages 167-177

    14. The hypoelliptic Laplacian of J.-M. Bismut

      • Gilles Lebeau
      Pages 179-194
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Keywords

Editors and Affiliations

  • Department of Mathematics, Kinki University, Higashi-Osaka, Japan

    Takashi Aoki

  • Department of Mathematics, Ochanomizu University, Tokyo, Japan

    Hideyuki Majima

  • Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Yoshitsugu Takei

  • Faculty of Economics, Keio University, Yokohama, Japan

    Nobuyuki Tose

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