Divergent formal solutions to Fuchsian partial differential equations

Masafumi YOSHINO

doi:10.2969/jmsj/04010139

Masafumi YOSHINO

著者情報

ジャーナルフリー

1988 年 40 巻 1 号 p. 139-150

DOI https://doi.org/10.2969/jmsj/04010139

詳細

Published: 1988 Received: 1986/02/13 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M.F. Atiyah, R. Bott and L. Garding, Lacunas for hyperbolic differential operators with constant coefficients I, Acta Math., 124 (1970), 109-189.
2) M.S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
3) G. Bengel and R. Gérard, Formal and convergent solutions of singular partial differential equations, Manuscripta Math., 38 (1982), 343-373.
4) L. Hörmander, The analysis of linear partial differential operators II, Springer, 1983.
5) J. Leray, Caractère non fredholmien du problème de Goursat, J. Math. Pures Appl., 53 (1974), 133-136.
6) J. Leray et C. Pisot, Une fonction de la théorie des nombres, J. Math. Pures Appl., 53 (1974), 137-145.
7) M. Kashiwara, T. Kawai and J. Sjöstrand, On a class of linear partial differential equations whose formal solutions always converge, Ark. Mat., 17 (1979), 83-91.
8) M. Yoshino, On sufficient conditions for convergence of formal solutions, Proc. Japan Acad., Ser. A, 61 (1985), 259-261.
9) M. Yoshino, On diophantine properties for convergence of formal solutions, Proc. Japan Acad., Ser. A, 62 (1986), 49-51.
10) M. Yoshino, The diophantine nature for convergence of formal solutions, (to be published in Tohoku J. Math.).
11) M. Zerner, Domaine d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C.R. Acad. Sci. Paris, 272 (1971), 1646-1648.

Right : [1] M. F. Atiyah, R. Bott and L. Gårding, Lacunas for hyperbolic differential operators with constant coefficients I, Acta Math., 124 (1970), 109-189.
[2] M. S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
[3] G. Bengel and R. Gérard, Formal and convergent solutions of singular partial differential equations, Manuscripta Math., 38 (1982), 343-373.
[4] L. Hörmander, The analysis of linear partial differential operators II, Springer, 1983.
[5] J. Leray, Caractère non fredholmien du problème de Goursat, J. Math. Pures Appl., 53 (1974), 133-136.
[6] J. Leray et C. Pisot, Une fonction de la théorie des nombres, J. Math. Pures Appl., 53 (1974), 137-145.
[7] M. Kashiwara, T. Kawai and J. Sjöstrand, On a class of linear partial differential equations whose formal solutions always converge, Ark. Mat., 17 (1979), 83-91.
[8] M. Yoshino, On sufficient conditions for convergence of formal solutions, Proc. Japan Acad., Ser. A, 61 (1985), 259-261.
[9] M. Yoshino, On diophantine properties for convergence of formal solutions, Proc. Japan Acad., Ser. A, 62 (1986), 49-51.
10) M. Yoshino, The diophantine nature for convergence of formal solutions, (to be published in Tôhoku J. Math.).
11) M. Zerner, Domaine d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris, 272 (1971), 1646-1648.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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