On the global existence of real analytic solutions of linear differential equations (I)

Takahiro KAWAI

doi:10.2969/jmsj/02430481

Takahiro KAWAI

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ジャーナルフリー

1972 年 24 巻 3 号 p. 481-517

DOI https://doi.org/10.2969/jmsj/02430481

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Published: 1972 Received: 1971/12/22 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Right : [1] K. G. Andersson Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat., 8 (1971), 277-302.
[2] K. G. Andersson Propagation of analyticity for solutions of differential equations of principal type, to appear in Bull. Amer. Math. Soc.
[1] M. F. Atiyah, R. Bott and L. Garding Lacunas for hyperbolic differential operators with constant coefficients I, Acta Math., 124 (1970), 109-189.
[1] E. De Giorgi and L. Cattabriga On the existence of analytic solutions on the whole real plane of linear partial differential equations with constant coefficients, to appear.
[2] E. De Giorgi and L. Cattabriga Una dimonstrazione diretta dell'esistenza di soluzioni analytiche nel piano reale di equazioni a derivate partiali a coefficienti constanti, Boll. Un. Mat. Ital., 4 (1971), 1015-1027.
[1] L. Ehrenpreis Solutions of some problems of division IV, Amer, J. Math., 82 (1960), 522-588.
[1] L. Hörmander Linear Partial Differential Operators, Springer, Berlin, 1963.
[2] L. Hörmander On the singularities of solutions of partial differential equations, Proc. Int. Conf. on Functional Analysis and Related Topics, Univ. of Tokyo Press, Tokyo, 1969, pp. 31-40.
[1] F. John Plane Waves and Spherical Means Applied to Partial Differential Equations, Interscience, New York, 1955.
[1] M. Kashiwara On the flabbiness of sheaf C. Sûrikaisekikenkyûsho Kôkyûroku, No. 114, Res. Inst. Math. Sci. Kyoto Univ., Kyoto, 1970, pp. 1-4. (In Japanese.)
[1] T. Kawai Theory of Fourier transformation in the theory of hyperfunctions and its applications, Master's thesis presented to Univ. of Tokyo, 1970. (In Japanese.)
[2] T. Kawai On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo, 17 (1970), 467-517.
[3] T. Kawai Construction of local elementary solutions for linear partial differential operators with real analytic coefficients (I)-The case with real principal symbols-, Publ. Res. Inst. Math. Sci. Kyoto Univ., 7 (1971), 363-396. Its summary is given in Proc. Japan Acad., 46 (1970), 912-916 and Proc. Japan Acad., 47 (1971), 19-24.
[4] T. Kawai Construction of local elementary solutions for linear partial differential operators with real analytic coefficients (II)-The case with complex principal symbols-, Publ. Res. Inst. Math. Sci. Kyoto Univ., 7 (1971), 397-424. Its summary is given in Proc. Japan Acad., 47 (1971), 147-152.
[5] T. Kawai A survey of the theory of linear (pseudo-) differential equations from the view point of phase functions-existence, regularity, effect of boundary conditions, transformations of operators, etc. Sûrikaisekikenkyûsho Kôkyûroku, No. 145, Res. Inst. Math. Sci. Kyoto Univ., Kyoto, 1971, pp. 157-167. (In Japanese.)
[6] T. Kawai On the global existence of real analytic solutions of linear differential equations, I, Proc. Japan Acad., 47 (1971), 537-540.
[7] T. Kawai On the global existence of real analytic solutions of linear differential equations,II, Proc. Japan Acad., 47 (1971), 643-647.
[8] T. Kawai On the global existence of real analytic solutions of linear differential equations, Lectures at the symposium on the theory of hyperfunctions and analytic functionals, Res. Inst. Math. Sci., 95, Technical Report of Res. Inst. Math. Sci. Kyoto Univ., 1971.
[1] H. Komatsu Relative cohomology of sheaves of solutions of differential equations, Seminaire Lions-Schwartz, 1966-67, reprinted in Reports of the Katata symposium on algebraic geometry and hyperfunctions, 1969, pp. 1-59.
[2] H. Komatsu Projective and injective limits of weakly compact sequences of locally convex spaces, J. Math. Soc. Japan, 19 (1967), 366-383.
[1] J. Leray Uniformalisation de la solution du problème linéaire analytique de Cauchy près de la variété qui porte les données de Cauchy (Problème de Cauchy I), Bull. Soc. Math. France, 85 (1957), 389-429.
[1] B. Malgrange Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier, 6 (1956), 271-355.
[1] A. Martineau Sur la topologie des espaces de fonctions holomorphes, Math. Ann., 163 (1966), 62-88.
[1] M. Sato Theory of hyperfunctions II, J. Fac. Sci. Univ. Tokyo, 8 (1960), 387-437.
[2] M. Sato Hyperfunctions and partial differential equations, Proc. Int. Conf. on Functional Analysis and Related Topics, Univ. of Tokyo Press, Tokyo, 1969, pp. 91-94.
[3] M. Sato Structures of hyperfunctions, Reports of the Katata symposium on algebraic geometry and hyperfunctions, 1969, pp. 4-1-4-30. (Notes by Kawai, in Japanese.)
[4] M. Sato Structure of hyperfunctions, Sûgaku no Ayumi, 15 (1970), 9-72. (Notes by Kashiwara, in Japanese.)
[5] M. Sato Regularity of hyperfunction solutions of partial differential equations, Proc. Nice Congress, 2, Gauthier-Villars, Paris, 1970, pp. 789-794.
[1] M. Sato, T. Kawai and M. Kashiwara Microfunctions and pseudo-differential equations, to appear in Proc. of Katata conference (Springer's lecture note). Its summary will appear in Proceedings of the symposium on partial differential equations held by Amer. Math. Soc. at Berkeley (1971).

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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