On the prolongation of local holomorphic solutions of partial differential equations

Yoshimichi TSUNO

doi:10.2969/jmsj/02630523

Yoshimichi TSUNO

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JOURNAL FREE ACCESS

1974 Volume 26 Issue 3 Pages 523-548

DOI https://doi.org/10.2969/jmsj/02630523

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Published: 1974 Received: July 26, 1973 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Yoshimichi TNUNO¹⁾
Right : Yoshimichi TSUNO¹⁾

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) G. Bengel, Sur le prolongement analytique des solutions d'une équation aux dérivées partielles, C. R. Acad. Sci. Paris, 273 (1971), 572-574.
2) J. M. Bony et P. Schapira, Sur le prolongement des solutions holomorphes d'équations aux dérivées partielles définies dans des ouverts convexes, C. R. Acad. Sci. Paris, 273 (1971), 360-363.
3) G. F. D. Duff, Partial differential equations, Toronto, 1956.
4) B. A. Fuks, Theory of analytic functions of several complex variables, Amer. Math. Soc. Transl. math. monograph, 8 (1963).
5) R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., 1965.
6) Y. Hamada, The singularities of the solutions of the Cauchy problem, Publ. RIMS, Kyoto Univ., 5 (1969), 21-40.
7) M. Hervé, Several complex variables, Local theory, Oxford Univ. Press, London, 1963.
8) L. Hörmander, Linear partial differential operators, Springer-Verlag, 1963.
9) T. Kawai, Construction of local elementary solutions for linear partial differential operators with real analytic coefficients (I), Publ. RIMS, Kyoto Univ., 7 (1971/72), 363-397.
10) C. O. Kiselman, Prolongement des solutions d'une équation aux dérivées partielles a coefficients constants, Bull. Soc. Math. France, 97 (1969), 329-356.
11) J. Morrow and K. Kodaira, Complex manifolds, Holt, Rinehart and Winston, Inc., 1971.
12) F. Trèves, Linear partial differential equations with constant coefficients, Gordon and Breach, 1966.
13) C. Wagschal, Problème de Cauchy analytique, a données méromorphes, J. Math. Pures Appl., 51 (1972), 375-397.
14) E. C. Zachmanoglou, Non-uniqueness of the Cauchy problem for linear partial differential equations with variable coefficients, Arch. Rational Mech. Anal., 27 (1968), 373-384.
15) E. C. Zachmanoglou, Uniqueness of the Cauchy problem for linear partial differential equations with variable coefficients, Trans. Amer. Math. Soc., 136 (1969), 517-526.
16) M. Zerner, Domaines d'holomorphie des fonctions verifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris, 272 (1971), 1646-1648.

Right : [1] G. Bengel, Sur le prolongement analytique des solutions d'une équation aux dérivées partielles, C. R. Acad. Sci. Paris, 273 (1971), 572-574.
[2] J. M. Bony et P. Schapira, Sur le prolongement des solutions holomorphes d'équations aux dérivées partielles définies dans des ouverts convexes, C. R. Acad. Sci. Paris, 273 (1971), 360-363.
[3] G. F. D. Duff, Partial differential equations, Toronto, 1956.
[4] B. A. Fuks, Theory of analytic functions of several complex variables, Amer. Math. Soc. Transl. math. monograph, 8 (1963).
[5] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., 1965.
[6] Y. Hamada, The singularities of the solutions of the Cauchy problem, Publ. RIMS, Kyoto Univ., 5 (1969), 21-40.
[7] M. Hervé, Several complex variables, Local theory, Oxford Univ. Press, London, 1963.
[8] L. Hörmander, Linear partial differential operators, Springer-Verlag, 1963.
[9] T. Kawai, Construction of local elementary solutions for linear partial differential operators with real analytic coefficients (I), Publ. RIMS, Kyoto Univ., 7 (1971/72), 363-397.
[10] C. O. Kiselman, Prolongement des solutions d'une équation aux dérivées partielles a coefficients constants, Bull. Soc. Math. France, 97 (1969), 329-356.
[11] J. Morrow and K. Kodaira, Complex manifolds, Holt, Rinehart and Winston, Inc., 1971.
[12] F. Trèves, Linear partial differential equations with constant coefficients, Gordon and Breach, 1966.
[13] C. Wagschal, Problème de Cauchy analytique, a données méromorphes, J. Math. Pures Appl., 51 (1972), 375-397.
[14] E. C. Zachmanoglou, Non-uniqueness of the Cauchy problem for linear partial differential equations with variable coefficients, Arch. Rational Mech. Anal., 27 (1968), 373-384.
[15] E. C. Zachmanoglou, Uniqueness of the Cauchy problem for linear partial differential equations with variable coefficients, Trans. Amer. Math. Soc., 136 (1969), 517-526.
[16] M. Zerner, Domaines d'holomorphie des fonctions verifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris, 272 (1971), 1646-1648.

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