TY - JOUR
T1 - Notes on the Cauchy-Kowalevski Theorem for E-modules
AU - Sugiki, Yuichi
AU - Takeuchi, Kiyoshi
PY - 2001/4/1
Y1 - 2001/4/1
N2 - 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.
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
KW - D-module
KW - Microlocal analysis
UR - http://www.scopus.com/inward/record.url?scp=0043241675&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0043241675&partnerID=8YFLogxK
U2 - 10.1006/jfan.2000.3707
DO - 10.1006/jfan.2000.3707
M3 - Article
AN - SCOPUS:0043241675
SN - 0022-1236
VL - 181
SP - 1
EP - 13
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -