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Fourier integral operators with complex-valued phase functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 459)

Keywords

  • Phase Function
  • Analytic Extension
  • Principal Symbol
  • Local Representative
  • Fourier Integral Operator

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References

  1. Duistermaat, J.J. and Hörmander, L., Fourier integral operators II. Acta Math., 128(1972), 183–269.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Duistermaat, J.J. and Sjöstrand, J., A global construction for pseudo-differential operators with non-involutive characteristics. Inventiones math., 20(1973), 209–225.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Hörmander, L., Fourier integral operators I. Acta Math., 127(1971), 79–183.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Hörmander, L., Lecture notes at the Nordic Summer School of Mathematics, 1969.

    Google Scholar 

  5. Hörmander, L., On the existence and the regularity of solutions of linear pseudo-differential operators. Enseignement Math., 17(1971), 99–163.

    MathSciNet  MATH  Google Scholar 

  6. Hörmander, L., Pseudo-differential operators and hypoelliptic equations. Amer. Math. Soc. Symp. on Singular Integral Operators, 1966, 138–183.

    Google Scholar 

  7. Hörmander, L., Pseudo-differential operators and non-elliptic boundary problems Ann. Math., 83(1966), 129–209.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Kucherenko, V.V., Hamilton-Jacobi equations in a complex non-analytic situation. Dokl. Akad. Nauk SSSR, 213(1973), 1021–1024.

    MathSciNet  Google Scholar 

  9. Kucherenko, V.V., Maslov’s canonical operator on a germ of complex, almost analytic manifold. Dokl. Akad. Nauk SSSR, 213(1973), 1251–1254.

    MathSciNet  Google Scholar 

  10. Leray, J., Le calcul différentiel et intégral sur une variété analytique complexe (Problème de Cauchy, III). Bull. Soc. math. France, 87(1959), 81–180.

    MathSciNet  MATH  Google Scholar 

  11. Maslov, V., The characteristics of pseudo-differential operators and difference schemes. Actes Congrès Intern. Math. Nice 1970, Tome 2, 755–769.

    Google Scholar 

  12. Nirenberg, L., A proof of the Malgrange preparation theorem. Proc. Liverpool Singularities Symp. I, Dept. pure Math. Univ. Liverpool 1969–1970, (1971), 97–105.

    Google Scholar 

  13. Nirenberg, L. and Treves, F., On local solvability of linear partial differential equations. Part I. Comm. Pure Appl. Math., 23(1970), 1–38.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Wells, R.O. Jr, Compact real submanifolds of a complex manifold with non-degenerate holomorphic tangent bundles. Math. Ann., 179(1969), 123–129.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1975 Springer-Verlag

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Melin, A., Sjöstrand, J. (1975). Fourier integral operators with complex-valued phase functions. In: Chazarain, J. (eds) Fourier Integral Operators and Partial Differential Equations. Lecture Notes in Mathematics, vol 459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074195

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  • DOI: https://doi.org/10.1007/BFb0074195

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07180-8

  • Online ISBN: 978-3-540-37521-0

  • eBook Packages: Springer Book Archive