Singularities of solutions of equations with noninvolutive characteristics-I the case of second order Fuchsian equations

Sunao OUCHI

doi:10.2969/jmsj/04520215

Singularities of solutions of equations with noninvolutive characteristics-I

the case of second order Fuchsian equations

Sunao OUCHI

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JOURNAL FREE ACCESS

1993 Volume 45 Issue 2 Pages 215-251

DOI https://doi.org/10.2969/jmsj/04520215

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Published: 1993 Received: October 19, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Singularities of solutions of equations with noninvolutive characteristics-I; the case of second order Fuchsian equations
Right : Singularities of solutions of equations with noninvolutive characteristics-I

Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Right : the case of second order Fuchsian equations

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. S. Bauoendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
2) S. Fujiie, On some degenerate elliptic equations of Fuchsian type with variable characteristic exponents (in Japanese), Kyoto Univ. master thesis, (1989).
3) Y. Hamada, The singularities of solutions of Cauchy problem, Publ. Res. Inst. Math. Sci., 5 (1969), 21-40.
4) Y. Hamada, J. Leray and C. Wagschal, Systèmes d'équations aux derivées partielles à caractéristiques multiples; problème de Cauchy ramifié; hyperbolicité partielle, J. Math. Pures Appl., 55 (1976), 297-352.
5) Y. Hasegawa, On the initial value problems with data on a characteristic hypersurface, J. Math. Kyoto Univ., 13 (1973), 579-593.
6) S. Ouchi, An integral representation of singular solutions of linear partial differential equations in the complex domain, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 27 (1980), 37-85.
7) S. Ouchi, An integral representation of singular solutions and removable singularities of solutions to linear partial differential equations, Publ. Res. Inst. Math. Sci., 26 (1990), 735-783.
8) H. Tahara, Fuchsian type equations and Fuchsian hyperbolic equations, Japan. J. Math. (N. S.), 5 (1979), 245-347.
9) J. Urabe, Meromorphic representations of the solutions of the singular Cauchy problems II, J. Math Kyoto Univ., 28 (1988), 335-342.
10) C. Wagschal, Problème de Cauchy analytique à données méromorphes, J. Math. Pures Appl., 51 (1972), 375-397.

Right : [1] M. S. Bauoendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
[2] S. Fujiie, On some degenerate elliptic equations of Fuchsian type with variable characteristic exponents (in Japanese), Kyoto Univ. master thesis, (1989).
[3] Y. Hamada, The singularities of solutions of Cauchy problem, Publ. Res. Inst. Math. Sci., 5 (1969), 21-40.
[4] Y. Hamada, J. Leray and C. Wagschal, Systèmes d'équations aux derivées partielles à caractéristiques multiples; problème de Cauchy ramifié; hyperbolicité partielle, J. Math. Pures Appl., 55 (1976), 297-352.
[5] Y. Hasegawa, On the initial value problems with data on a characteristic hypersurface, J. Math. Kyoto Univ., 13 (1973), 579-593.
[6] S. Ouchi, An integral representation of singular solutions of linear partial differential equations in the complex domain, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 27 (1980), 37-85.
[7] S. Ouchi, An integral representation of singular solutions and removable singularities of solutions to linear partial differential equations, Publ. Res. Inst. Math. Sci., 26 (1990), 735-783.
[8] H. Tahara, Fuchsian type equations and Fuchsian hyperbolic equations, Japan. J. Math. (N. S.), 5 (1979), 245-347.
[9] J. Urabe, Meromorphic representations of the solutions of the singular Cauchy problems II, J. Math Kyoto Univ., 28 (1988), 335-342.
[10] C. Wagschal, Problème de Cauchy analytique à données méromorphes, J. Math. Pures Appl., 51 (1972), 375-397.

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