On microhyperbolic mixed problems

Kiyômi KATAOKA; Nobuyuki TOSE

doi:10.2969/jmsj/04320261

Kiyômi KATAOKA, Nobuyuki TOSE

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 2 Pages 261-304

DOI https://doi.org/10.2969/jmsj/04320261

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Published: 1991 Received: October 05, 1989 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: AUTHOR Details: Wrong : Kyomi KATAOKA¹⁾, Nobuyuki TOSE²⁾
Right : Kiyômi KATAOKA¹⁾, Nobuyuki TOSE²⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J.M. Bony and P. Schapira, Propagation des singularités analytiques pour les solutions des équations aux derivées partielles, Ann. Inst. Fourier, Grenoble, 26 (1976), 81-140.
2) R. Hartshorne, Residues and Duality, Lecture Notes in Math., 20, Springer, 1966.
3) K. Kajitani and S. Wakabayashi, The hyperbolic mixed problem in Gevrey classes, Japan. J. Math., 15 (1989), 309-383.
4) M. Kashiwara and T. Kawai, On the boundary value problem for elliptic system of linear differential equations I, Proc. Japan Acad., 48 (1972), 712-715.
5) M. Kashiwara and T. Kawai, On the boundary value problem for elliptic system of linear differential equations II, Proc. Japan Acad., 49 (1973), 164-168.
6) M. Kashiwara and T. Kawai, On microhyperbolic pseudo-differential operators I, J. Math. Soc. Japan, 27 (1975), 359-404.
7) M. Kashiwara and Y. Laurent, Théoremès d'annulation et deuxième microlocalisation, Prépublication d'Orsay, Univ. Paris-Sud, 1983.
8) M. Kashiwara and P. Schapira, Micro-hyperbolic systems, Acta Math., 142 (1979), 1-55.
9) M. Kashiwara and P. Schapira, Microlocal Study of Sheaves, Astérisques, 128 (1985).
10) M. Kashiwara and P. Schapira Sheaves on Manifolds, Grundl, d. math. Wiss. Bd. 292, Springer, 1990.
11) K. Kataoka, Micro-local theory of boundary value problems I, J. Fac. Sci. Univ. Tokyo, Sect IA, 27 (1980), 355-399.
12) K. Kataoka, Micro-local theory of boundary value problems II, J. Fac. Sci. Univ. Tokyo, Sect IA, 28 (1981), 31-56.
13) K. Kataoka, On the theory of Radon transformations of hyperfunctions, J. Fac. Sci. Univ. Tokyo, Sect IA, 28 (1981), 331-412.
14) H. Komatsu and T. Kawai, Boundary values of hyperfunction solutions of linear partial differential equations, Publ. Res. Inst. Math. Sci., 7 (1971), 95-104.
15) A. Martinez, Prolongement des solutions holomorphes de problèmes aux limites, Ann. Inst. Fourier, Grenoble, 35 (1985), 93-116.
16) R. Sakamoto, E-wellposedness for hyperbolic mixed problems with constant coefficients, J. Math. Kyoto Univ., 14 (1974), 93-118.
17) M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations, lecture Notes in Math., 287, Springer, 1973, pp. 265-529.
18) P. Schapira, Théorie des hyperfonctions, Lecture Notes in Math., 126, Springer, 1970.
19) P. Schapira, Hyperfonctions et problèmes aux limites elliptiques, Bull. Soc. Math. France, 99 (1971), 113-141.
20) P. Schapira, Propagation au bord et réflexion des singularités analytiques des solutions des équations aux dérivées partielles, Sém. Goulaouic-Schwartz, 1975-1976, exposé 6.
21) P. Schapira, Propagation au bord et réflexion des singularités analytiques des solutions des équations aux dérivées partielles, II. Sém. Goulaouic-Schwartz, 1976-1977, exposé 9.
22) P. Schapira, Front d'onde analytiques au bord I, C.R. Acad. Sci. Paris, 302, Série I, n° 10 (1986), 383-386.
23) P. Schapira, Front d'onde analytiques au bord II, Sém. Equations aux Derivées Partielles, 1985-1986, exposé 13, École Polytechnique.
24) P. Schapira and G. Zampieri, Microfunctions at the boundary and mild microfunctions, Publ. Res. Inst. Math. Sci., Kyoto Univ., 24 (1988), 495-503.
25) J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems, Comm. P.D.E., 5(1) (1980), 41-94.
26) J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems, II, Comm. P.D.E., 5(2) (1980), 187-207.
27) J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems, III, Comm. P.D.E., 6(5) (1981), 499-567.
28) J. Sjöstrand,Analytic singularities and microhyperbolic boundary value problems, Math. Ann., 254 (1980), 211-256.
29) N. Tose, Microlocal boundary value problems for partially elliptic systems of micro-differential equations, Master thesis presented to Univ. of Tokyo (in Japanese), 1985.
30) N. Tose and M. Uchida, Boundary value problems for partially elliptic systems and their applications, in preparation.
31) M. Kashiwara, Algebraic study of systems of partial differential equations, Master thesis, Univ. of Tokyo, 1971 (in Japanese).

Right : [1] J. M. Bony and P. Schapira, Propagation des singularités analytiques pour les solutions des équations aux derivées partielles, Ann. Inst. Fourier, Grenoble, 26 (1976), 81-140.
[2] R. Hartshorne, Residues and Duality, Lecture Notes in Math., 20, Springer, 1966.
[3] K. Kajitani and S. Wakabayashi, The hyperbolic mixed problem in Gevrey classes, Japan. J. Math., 15 (1989), 309-383.
[4] M. Kashiwara and T. Kawai, On the boundary value problem for elliptic system of linear differential equations I, Proc. Japan Acad., 48 (1972), 712-715.
[5] M. Kashiwara and T. Kawai, On the boundary value problem for elliptic system of linear differential equations II, Proc. Japan Acad., 49 (1973), 164-168.
[6] M. Kashiwara and T. Kawai, On microhyperbolic pseudo-differential operators I, J. Math. Soc. Japan, 27 (1975), 359-404.
[7] M. Kashiwara and Y. Laurent, Théorèmes d'annulation et dzuxième microlocalisation, Prépublication d'Orsay, Univ. Paris-Sud, 1983.
[8] M. Kashiwara and P. Schapira, Micro-hyperbolic systems, Acta Math., 142 (1979), 1-55.
[9] M. Kashiwara and P. Schapira, Microlocal Study of Sheaves, Astérisques, 128 (1985).
[10] M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundl. d. math. Wiss. Bd. 292, Springer, 1990.
[11] K. Kataoka, Micro-local theory of boundary value problems I, J. Fac. Sci. Univ. Tokyo, Sect IA, 27 (1980), 355-399.
[12] K. Kataoka, Micro-local theory of boundary value problems II, J. Fac. Sci. Univ. Tokyo, Sect IA, 28 (1981), 31-56.
[13] K. Kataoka, On the theory of Radon transformations of hyperfunctions, J. Fac. Sci. Univ. Tokyo, Sect IA, 28 (1981), 331-412.
[14] H. Komatsu and T. Kawai, Boundary values of hyperfunction solutions of linear partial differential equations, Publ. Res. Inst. Math. Sci., 7 (1971), 95-104.
[15] A. Martinez, Prolongement des solutions holomorphes de problèmes aux limites, Ann. Inst. Fourier, Grenoble, 35 (1985), 93-116.
[16] R. Sakamoto, ε-wellposedness for hyperbolic mixed problems with constant coefficients, J. Math. Kyoto Univ., 14 (1974), 93-118.
[17] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations, lecture Notes in Math., 287, Springer, 1973, pp. 265-529.
[18] P. Schapira, Théorie des hyperfonctions, Lecture Notes in Math., 126, Springer, 1970.
[19] P. Schapira, Hyperfonctions et problèmes aux limites elliptiques, Bull. Soc. Math. France, 99 (1971), 113-141.
[20] P. Schapira, Propagation au bord et réflexion des singularités analytiques des solutions des équations aux dérivées partielles, Sém. Goulaouic-Schwartz, 1975-1976, exposé 6.
[21] P. Schapira, Propagation au bord et réflexion des singularités analytiques des solutions des équations aux dérivées partielles, II. Sém. Goulaouic-Schwartz, 1976-1977, exposé 9.
[22] P. Schapira, Front d'onde analytiques au bord I, C. R. Acad. Sci. Paris, 302, Série I, n° 10 (1986), 383-386.
[23] P. Schapira, Front d'onde analytiques au bord II, Sém. Equations aux Derivées Partielles, 1985-1986, exposé 13, École Polytechnique.
[24] P. Schapira and G. Zampieri, Microfunctions at the boundary and mild microfunctions, Publ. Res. Inst. Math. Sci., Kyoto Univ., 24 (1988), 495-503.
[25] J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems, Comm. P. D. E., 5(1) (1980), 41-94.
[26] J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems, II, Comm. P. D. E., 5 (2) (1980), 187-207.
[27] J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems, III, Comm. P. D. E., 6 (5) (1981), 499-567.
[28] J. Sjöstrand,Analytic singularities and microhyperbolic boundary value problems, Math. Ann., 254 (1980), 211-256.
[29] N. Tose, Microlocal boundary value problems for partially elliptic systems of micro-differential equations, Master thesis presented to Univ. of Tokyo (in Japanese), 1985.
[30] N. Tose and M. Uchida, Boundary value problems for partially elliptic systems and their applications, in preparation.
[31] M. Kashiwara, Algebraic study of systems of partial differential equations, Master thesis, Univ. of Tokyo, 1971 (in Japanese).

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