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On the global existence of real analytic solutions of linear differential equations

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Hyperfunctions and Pseudo-Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 287))

This work has been supported in part by the Sakkokai Foundation.

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References

  1. Andersson, K. G.: Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat., 8 (1971), 277–302.

    Article  MathSciNet  Google Scholar 

  2. Bruhat, Y.: Hyperbolic partial differential equations on a manifold, Proc. of Battelle Recontres, Benjamin, New York, 1968, pp.84–106.

    Google Scholar 

  3. De Giorgi, E. and L. Cattabriga: On the existence of analytic solutions on the whole real plane of linear partial differential equations with constant coefficients, to appear.

    Google Scholar 

  4. : Una dimonstrazione diretta dell’esistenza di soluzioni analytiche nel piano reale di equazioni a derivate partiali a coefficienti constanti, Bol. Un. Mat. Ital., 4 (1971), 1015–1027.

    Google Scholar 

  5. Egorov, Yu. V.: Conditions for the solvability of pseudo-differential operators, Dokl. Akad. Nauk USSR, 187 (1969), 1232–1234.

    Google Scholar 

  6. Ehrenpreis, L.: Some applications of the theory of distributions to several complex variables, Seminar on Analytic Functions, Princeton, 1957, pp.65–79.

    Google Scholar 

  7. : Solutions of some problems of division IV, Amer. J. Math., 82 (1960), 522–588.

    Article  MathSciNet  Google Scholar 

  8. : Fourier Analysis in Several Complex Variables, Wiley-Interscience, New York, 1970.

    MATH  Google Scholar 

  9. Hörmander, L.: Linear Partial Differential Operators, Springer, Berlin, 1963.

    Book  Google Scholar 

  10. : Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients, Comm. Pure Appl. Math., 24 (1971), 671–704.

    Article  MathSciNet  Google Scholar 

  11. : On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math., 17 (1971), 99–163.

    MathSciNet  MATH  Google Scholar 

  12. John, F.: Plane Waves and Spherical Means Applied to Partial Differential Equations, Interscience, New York, 1955.

    MATH  Google Scholar 

  13. Kashiwara, M.: On the flabbiness of sheaf e, Sûrikaiseki Kenkyûsho Kôkyûroku, No.114, R.I.M.S. Kyoto Univ., 1970, pp.1–4 (in Japanese).

    Google Scholar 

  14. Kashiwara, M. and T. Kawai: Pseudo-differential operators in the theory of hyperfunctions, Proc. Japan Acad., 46 (1970), 1130–1134.

    Article  MathSciNet  Google Scholar 

  15. : Pseudo-differential operators in the theory of hyperfunctions, Proc. Japan Acad., 46 (1970), 1130–1134. in preparation.

    Article  MathSciNet  Google Scholar 

  16. Kawai, T.: Construction of local elementary solutions for linear partial differential operators with real analytic coefficients (I) — The case with real principal symbols —, Publ. R.I.M.S. Kyoto Univ., 7 (1971), 363–397. Its summary is given in Proc. Japan Acad., 46 (1970), 912–916 and 47 (1971), 19–24.

    Article  MathSciNet  Google Scholar 

  17. : Construction of local elementary solutions for linear partial differential operators with real analytic coefficients II. — The case with complex principal symbols —, Publ. R.I.M.S. Kyoto Univ., 7 (1971), 399–424. Its summary is given in Proc. Japan Acad., 47 (1971), 147–152.

    Article  MathSciNet  Google Scholar 

  18. —: 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. Reports of the Symposium on the Theory of Hyperfunctions and Differential Equations, R.I.M.S. Kyoto Univ., 1971, pp.84–92 (in Japanese).

    Google Scholar 

  19. : On the global existence of real analytic solutions of linear differential equations. I, Proc. Japan Acad., 47 (1971), 537–540.

    Article  MathSciNet  Google Scholar 

  20. : On the global existence of real analytic solutions of linear differential equations. II, Proc. Japan Acad., 47 (1971), 643–647.

    MathSciNet  MATH  Google Scholar 

  21. —: On the global existence of real analytic solutions of linear differential equations (I), J. Math. Soc. Japan, 24 (1972) to appear, (II), …, in preparation.

    Google Scholar 

  22. Komatsu, H.: Relative cohomology of sheaves of solutions of differential equations, Séminaire Lions-Schwartz, 1966, Reprinted in these Proceedings.

    Google Scholar 

  23. : Resolutions by hyperfunctions of sheaves of solutions of differential equations with constant coefficients, Math. Ann., 176 (1968), 77–86.

    Article  MathSciNet  Google Scholar 

  24. Leray, J.: Hyperbolic Partial Differential Equations, Mimeographed notes, Princeton, 1952.

    Google Scholar 

  25. : Uniformisation 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.

    Article  MathSciNet  Google Scholar 

  26. Malgrange, B.: Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier Grenoble, 6 (1955), 271–355.

    Article  MathSciNet  Google Scholar 

  27. Nirenberg, L. and F. Treves: On local solvability of linear partial differential equations, Part II: Sufficient conditions, Comm. Pure Appl. Math., 23 (1970), 459–501.

    Article  MathSciNet  Google Scholar 

  28. Palamodov, V. P.: Linear Differential Operators with Constant Coefficients, Springer, Berlin, 1970. Translation from the Russian original, which was published in 1967 by Nauka.

    Book  Google Scholar 

  29. Sato, M.: Theory of hyperfunctions II, J. Fac. Sci. Univ. Tokyo, Sect. I, 8 (1960), 387–437.

    MathSciNet  MATH  Google Scholar 

  30. : Hyperfunctions and partial differential equations, Proc. Intern. Conf. on Functional Analysis and Related Topics, Univ. of Tokyo Press, Tokyo, 1969, pp.91–94.

    Google Scholar 

  31. —: Structure of hyperfunctions, Reports of the Katata Symp. on algebraic geometry and hyperfunctions, 1969, pp.4.1–30 (notes by Kawai, in Japanese).

    Google Scholar 

  32. : Structure of hyperfunctions, Sûgaku no Ayumi, 15 (1970), 9–72 (notes by Kashiwara, in Japanese).

    Google Scholar 

  33. : Regularity of hyperfunction solutions of partial differential equations, Proceedings of Nice Congress, 2, Gauthier-Villars, Paris, 1971, pp.785–794.

    Google Scholar 

  34. Sato, M., T. Kawai and M. Kashiwara: On pseudo-differential equations in hyperfunction theory, these proceedings. Its summary is given in Proceedings of the Symposium on Partial Differential Equations held by A.M.S. at Berkeley, 1971.

    Google Scholar 

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Japan

    Takahiro Kawai

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  1. Takahiro Kawai
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Hikosaburo Komatsu

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© 1973 Springer-Verlag

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Kawai, T. (1973). On the global existence of real analytic solutions of linear differential equations. In: Komatsu, H. (eds) Hyperfunctions and Pseudo-Differential Equations. Lecture Notes in Mathematics, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068147

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  • DOI: https://doi.org/10.1007/BFb0068147

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06218-9

  • Online ISBN: 978-3-540-38506-6

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