A sharp sufficient geometric condition for the existence of global real analytic solutions on a bounded domain

Akira KANEKO

doi:10.2969/jmsj/03910163

Akira KANEKO

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 1 Pages 163-170

DOI https://doi.org/10.2969/jmsj/03910163

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Published: 1987 Received: November 21, 1984 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: CITATION Details: Wrong : 1) K. G. Andersson, Propagation of analyticity of solutions of partial differential equations with constant coefficients, Arkiv för Mat., 8 (1971), 277-302.
2) K. G. Andersson, Global solvability of partial differential equations in the space of real analytic functions, Coll, on Analysis, Rio de Janeiro, August, 1972, Analyse fonctionelle, Hermann, Paris, 1974.
3) L. Cattabriga, Sull'esistenza di soluzioni analitiche reali di equationi a derivate parziali a coefficients costanti, Boll. Un. Mat. Ital. (4), 12 (1975), 221-234.
4) J. W. de Roever, Hyperfunctional singular support of ultradistributions, J. Fac. Sci. Univ. Tokyo Sect. IA, 31 (1985), 585-631.
5) L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math., 21 (1973), 151-182.
6) A. Kaneko, On the global existence of real analytic solutions of linear partial differential equations on unbounded domain, J. Fac. Sci. Univ. Tokyo Sect. IA, 32 (1985), 319-372.
7) T. Kawai, On the global existence of real analytic solutions of linear differential equations (I), J. Math. Soc. Japan, 24 (1972), 481-517.
8) H. Komatsu, Resolution by hyperfunctions of sheaves of solutions of differential equations with constant coefficients, Math. Ann., 176 (1968), 77-86.
9) M. Sato, T. Kawai and M. Kashiwara (S-K-K), Hyperfunctions and pseudo-differential equations, Lecture Notes in Math., 287, Springer, 1973, pp. 263-529.
10) G. Zampieri, Propagation of singularity and existence of real analytic solutions of locally hyperbolic equations, J. Fac. Sci. Univ. Tokyo Sect. IA, 31 (1984), 373-390.
11) G. Zampieri, Personal correspondence, June 1983.

Right : [1] K. G. Andersson, Propagation of analyticity of solutions of partial differential equations with constant coefficients, Arkiv för Mat., 8 (1971), 277-302.
[2] K. G. Andersson, Global solvability of partial differential equations in the space of real analytic functions, Coll. on Analysis, Rio de Janeiro, August, 1972, Analyse fonctionelle, Hermann, Paris, 1974.
[3] L. Cattabriga, Sull'esistenza di soluzioni analitiche reali di equationi a derivate parziali a coefficienti costanti, Boll. Un. Mat. Ital. (4), 12 (1975), 221-234.
[4] J. W. de Roever, Hyperfunctional singular support of ultradistributions, J. Fac. Sci. Univ. Tokyo Sect. IA, 31 (1985), 585-631.
[5] L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math., 21 (1973), 151-182.
[6] A. Kaneko, On the global existence of real analytic solutions of linear partial differential equations on unbounded domain, J. Fac. Sci. Univ. Tokyo Sect. IA, 32 (1985), 319-372.
[7] T. Kawai, On the global existence of real analytic solutions of linear differential equations (I), J. Math. Soc. Japan, 24 (1972), 481-517.
[8] H. Komatsu, Resolution by hyperfunctions of sheaves of solutions of differential equations with constant coefficients, Math. Ann., 176 (1968), 77-86.
[9] M. Sato, T. Kawai and M. Kashiwara (S-K-K), Hyperfunctions and pseudo-differential equations, Lecture Notes in Math., 287, Springer, 1973, pp. 263-529.
[10] G. Zampieri, Propagation of singularity and existence of real analytic solutions of locally hyperbolic equations, J. Fac. Sci. Univ. Tokyo Sect. IA, 31 (1984), 373-390.
[11] G. Zampieri, Personal correspondence, June 1983.

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