Notes on the Cauchy-Kowalevski Theorem for E-modules

Yuichi Sugiki, Kiyoshi Takeuchi

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For a coherent EX-module M, Kashiwara and Schapira introduced the complex RHomEX(M, OX) of holomorphic solutions to M. Very recently this complex was used by R. Ishimura (1998, J. Math. Pures Appl.77, 647-654) to formulate and establish the Cauchy-Kowalevski theorem for E-modules. In this paper, we will give a rigorous proof of some arguments of Ishimura.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalJournal of Functional Analysis
Issue number1
Publication statusPublished - 2001 Apr 1


  • Cauchy problem
  • D-module
  • Microlocal analysis

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