Notes on the Cauchy-Kowalevski Theorem for E-modules

Yuichi Sugiki; Kiyoshi Takeuchi

doi:10.1006/jfan.2000.3707

Notes on the Cauchy-Kowalevski Theorem for E-modules

Research output: Contribution to journal › Article › peer-review

Abstract

For a coherent E_X-module M, Kashiwara and Schapira introduced the complex RHom_EX(M, O_X) 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 language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Journal of Functional Analysis
Volume	181
Issue number	1
DOIs	https://doi.org/10.1006/jfan.2000.3707
Publication status	Published - 2001 Apr 1
Externally published	Yes

Keywords

Cauchy problem
D-module
Microlocal analysis

ASJC Scopus subject areas

Analysis

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10.1006/jfan.2000.3707

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abstract = "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.",

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author = "Yuichi Sugiki and Kiyoshi Takeuchi",

year = "2001",

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AB - 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.

KW - Cauchy problem

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KW - Microlocal analysis

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Notes on the Cauchy-Kowalevski Theorem for E-modules

Abstract

Keywords

ASJC Scopus subject areas

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