Skip to main content
Log in

Fourier integral operators. II

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Andersson, K. G., Propagation of analyticity of solutions of partial differential equations with constant coefficients.Ark. Mat. 8 (1970), 277–302.

    MathSciNet  Google Scholar 

  2. Birkhoff, G. D.,Dynamical systems. Amer. Math. Soc. Coll. Publ. 9, New York, 1927.

  3. Bourbaki, N.,Espaces vectoriels topologiques. Paris, 1953–55.

  4. Bjorken, J. D. &Drell, S.,Relativistic quantum fields. Mc Graw-Hill, New York, 1965.

    MATH  Google Scholar 

  5. Courant, R. &Lax, P. D., The propagation of discontinuities in wave motion.Proc. Nat. Acad. Sci. USA 42 (1956), 873–876.

    Article  MathSciNet  Google Scholar 

  6. DeWitt, B. S., Dynamical theory of groups and fields.Relativity, groups and topology, 585–820. Gordon and Breach, New York-London 1964.

    Google Scholar 

  7. Dieudonne, J. &Schwartz, L., La dualité dans les espaces (£) et (ℒ£).Ann. Inst. Fourier (Grenoble), 1 (1949), 61–101.

    MathSciNet  MATH  Google Scholar 

  8. Dugundji, J. &Antosiewicz, H. A., Parallelizable flows and Lyapunov's second method.Ann. of Math. 73 (1961), 543–555.

    Article  MathSciNet  Google Scholar 

  9. Gårding, L., Kotake, T. &Leray, J., Uniformisation et développement asymptotique de la solution du problème de Cauchy linéaire, à données holomorphes; analogie avec la théorie des ondes asymptotiques et approchées (Problème de Cauchy Ibis et VI).Bull. Soc. Math. France, 92 (1964), 263–361.

    MathSciNet  MATH  Google Scholar 

  10. Grušin, V. V., The extension of smoothness of solutions of differential equations of principal type.Dokl. Akad. Nauk SSSR, 148 (1963), 1241–1244. Also inSoviet Math. Dokl. 4 (1963), 248–252.

    MathSciNet  Google Scholar 

  11. Hadamard, J.,Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques. Hermann, Paris 1932.

    Google Scholar 

  12. Haefliger, A., Variétés feuilletées.Ann. Scuola Norm. Sup. Pisa, 16 (1962), 367–397.

    MathSciNet  MATH  Google Scholar 

  13. Hörmander, L.,Introduction to complex analysis in several variables. D. van Nostrand Publ. Co., Princeton, N. J. 1965.

    Google Scholar 

  14. —, Pseudo-differential operators and non-elliptic boundary problems.Ann. of Math., 83 (1966), 129–209.

    Article  MathSciNet  Google Scholar 

  15. —, On the singularities of solutions of partial differential equations.Comm. Pure Appl. Math. 23 (1970), 329–358.

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  17. —, Linear differential operators.Actes Congr. Intern. Math. Nice, 1970, 1, 121–133.

    Google Scholar 

  18. —, On the existence and the regularity of solutions of linear pseudo-differential equations.L'Enseignement Math. 17 (1971), 99–163.

    MATH  Google Scholar 

  19. Palais, R., A global formulation of the Lie theory of transformation groups.Mem. Amer. Math. Soc., 22 (1957).

  20. Malgrange,B., Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution.Ann. Inst. Fourier (Grenoble), 6 (1955–56), 271–355.

  21. Riesz, M., L'intégrale de Riemann-Liouville et le problème de Cauchy.Acta Math., 81 (1949), 1–223.

    Article  MathSciNet  Google Scholar 

  22. Steenrod, N.,The topology of fiber bundles. Princeton Univ. Press, Princeton 1951.

    Google Scholar 

  23. Unterberger, A. &Bokobza, J., Les opérateurs pseudo-différentiels d'ordre variable.C. R. Acad. Sci. Paris, 261 (1965), 2271–2273.

    MathSciNet  MATH  Google Scholar 

  24. Whitney, H., Regular families of curves.Ann. of Math., 34 (1933), 244–270.

    Article  MathSciNet  Google Scholar 

  25. Zerner, M., Solutions singulières d'équations aux dérivées partielles.Bull. Soc. Math. France, 91 (1963), 203–226.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by NSF Grant GP-27176 at Courant Institute, New York University, NSF Grant GP-7952X2 at the Institute for Advanced Study, Princeton, and AFOSR contract F44620-69-C-0106 at Stanford University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Duistermaat, J.J., Hörmander, L. Fourier integral operators. II. Acta Math. 128, 183–269 (1972). https://doi.org/10.1007/BF02392165

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392165

Keywords

Navigation