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Analytic hypo-ellipticity and propagation of regularity for a system of microdifferential equations with non-involutory characteristics

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References

  1. Boutet de Monvel, L.: Hypoelliptic operators with double characteristics and related pseudodifferential operators. Comm. Pure Appl. Math.27, 585–639 (1974)

    Google Scholar 

  2. Boutet de Monvel, L., Treves, F.: On a class of pseudodifferential operators with double characteristics. Invent. Math.24, 1–34 (1974)

    Google Scholar 

  3. Boutet de Monvel, L., Treves, F.: On a class of systems of pseudodifferential equations with double characteristics. Comm. Pure Appl. Math.27, 59–89 (1974)

    Google Scholar 

  4. Grušin, V.V.: On a class of hypoelliptic operators. Math. USSR-Sb.12, 458–476 (1970)

    Google Scholar 

  5. Grušin, V. V.: On a class of elliptic pseudodifferential operators degenerate on a submanifold. Math. USSR-Sb.13, 155–185 (1971)

    Google Scholar 

  6. Hörmander, L.: A class of hypoelliptic pseudodifferential operators with double characteristics. Math. Ann.217, 165–188 (1975)

    Google Scholar 

  7. Kashiwara, M., Kawai, T.: Some applications of boundary value problems for elliptic systems of linear differential equations. In: Ann. of Math. Studies No. 93, pp. 39–61. Princeton: Princeton University Press 1979

    Google Scholar 

  8. Kashiwara, M., Kawai, T., Oshima, T.: Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics. I, II. Proc. Japan Acad.50, 420–425; 549–550 (1974).

    Google Scholar 

  9. Kashiwara, M., Kawai, T., Oshima, T.: Structure of a single pseudo-differential equation in a real domain. J. Math. Soc. Japan28, 80–85 (1976)

    Google Scholar 

  10. Kataoka, K.: On the theory of Radon transformations of hyperfunctions. J. Fac. Sci. Univ. Tokyo Sect. IA Math.28, 331–413 (1981)

    Google Scholar 

  11. Kataoka, K.: Micro-local theory of boundary value problems I. J. Fac. Sci. Univ. Tokyo Sect. IA Math.27, 355–399 (1980)

    Google Scholar 

  12. Melin, A., Sjöstrand, J.: Fourier integral operators with complex-valued phase functions. In: Lecture Notes in Mathematics, Vol. 459, pp. 120–223. Berlin, Heidelberg, New York: Springer 1975

    Google Scholar 

  13. Melin, A., Sjöstrand, J.: Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem. Comm. Partial Differential Equations1, 313–400 (1976)

    Google Scholar 

  14. Métivier, G.: Hypoellipticité analytique sur des groupes nilpotents de rang 2. Duke Math. J.47, 195–221 (1980)

    Google Scholar 

  15. Métivier, G.: Analytic hypoellipticity for operators with multiple characteristics. Comm. Partial Differential Equations6, 1–90 (1981)

    Google Scholar 

  16. Ôaku, T.: A canonical form of a system of microdifferential equations with non-involutory characteristics and branching of singularities. Invent. Math.65, 491–525 (1982)

    Google Scholar 

  17. Ôaku, T.: Analytic hypo-ellipticity of a system of microdifferential equations with noninvolutory characteristics. Proc. Japan Acad.57, 438–441 (1981)

    Google Scholar 

  18. Ôaku, T.: Analytic hypo-ellipticity and propagation of regularity for operators with noninvolutory characteristics. Proc. Japan Acad.58, 51–54 (1982)

    Google Scholar 

  19. Sato, M., Kawai, T., Kashiwara, M.: Microfunctions and pseudo-differential equations. In: Lecture Notes in Mathematics, Vol. 287, pp. 265–529. Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  20. Sato, M., Kawai, T., Kashiwara, M.: On the structure of single linear pseudo-differential equations. Proc. Japan Acad.48, 43–646 (1972)

    Google Scholar 

  21. Schapira, P.: Conditions de positivité dans une variété symplectique complexe. Application à l'étude des microfonctions. Ann. Sci. École Norm. Sup. (4)14, 121–139 (1981)

    Google Scholar 

  22. Sjöstrand, J.: Parametrices for pseudodifferential operators with multiple characteristics. Ark Mat.12, 85–130 (1974)

    Google Scholar 

  23. Tahara, H.: Fuchsian type equations and Fuchsian hyperbolic equations. Japan. J. Math.5 245–347 (1979)

    Google Scholar 

  24. Tartakoff, D. S.: The local real analyticity of solutions to □ b and the\(\bar \partial\)-Neumann problem Acta Math.145, 177–204 (1981)

    Google Scholar 

  25. Treves, F.: Analytic hypo-ellipticity of a class of pseudodifferential operators with doubk characteristics and applications to the\(\bar \partial\)-Neumann problem. Comm. Partial Differential Equations3, 475–642 (1978)

    Google Scholar 

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  1. Department of Mathematics, University of Tokyo, Hongo, 113, Tokyo, Japan

    Toshinori Ôaku

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  1. Toshinori Ôaku
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Ôaku, T. Analytic hypo-ellipticity and propagation of regularity for a system of microdifferential equations with non-involutory characteristics. Math. Ann. 269, 145–168 (1984). https://doi.org/10.1007/BF01451415

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