Article PDF
Avoid common mistakes on your manuscript.
References
Arnold, V. I., On a characteristic class which enters in quantization conditions.Funkt. anal. i ego pril., 1 (1967), 1–14 (Russian.). English translationFunct. anal. appl., 1 (1967), 1–13.
Atiyah, M. F.,K-theory. Benjamin 1968.
Atiyah, M. F. &Bott, R., A Lefschetz fixed point formula, for elliptic complexes I.Ann. of Math., 86 (1967), 374–407.
Bokobza-Haggiag, J., Opérateurs pseudo-différentiels sur une variété différentiable.Ann. Inst. Fourier, Grenoble, 19 (1969), 125–177.
Buslaev, V. S., The generating integral and the canonical Maslov operator in the WKB method,Funkt anal. i ego pril., 3:3 (1969), 17–31 (Russian). English translationFunct. anal. appl., 3 (1969), 181–193.
Carathéodory, C.,Variationsrechnung und partielle Differentialgleichungen Erster Ordnung. Teubner, Berlin, 1935.
Egorov, Yu. V., On canonical transformations of pseudo-differential operators.Uspehi Mat. Nauk. 25 (1969), 235–236.
—, On non-degenerate hypoelliptic pseudo-differential operators.Doklady Akad. Nauk SSSR. 186 (1969), 1006–1007. (Russian.) English translationSoviet Math. Doklady, 10 (1969), 697–699.
Eškin, G. I., The Cauchy problem for hyperbolic systems in convolutions.Mat. Sbornik, 74 (116) (1967), 262–297 (Russian). English translationMath. USSR — Sbornik, 3 (1967), 243–277.
Friedrichs, K.,Pseudo-differential operators. An introduction. Lecture notes, Courant Institute, New York University 1968.
Hirzebruch, P.,Topological methods in algebraic geometry. Grundlehren der Math. Wiss. 131, Springer-Verlag 1966.
Hörmander, L., Pseudo-differential operators,Comm. Pure Appl. Math., 18 (1965), 501–517.
—, Pseudo-differential operators and hypoelliptic equations.Amer. Math. Soc. Symp. Pure Math., 10 (1966), Singular integral operators, 138–183.
—, The spectral function of an elliptic operator.Acta Math., 121 (1968) 193–218.
Hörmander, L., On the singularities of solutions of partial differential equations.Conf. on Funct. Anal. and Related Topics, Tokyo 1969, 31–40.
Hörmander, L., The calculus of Fourier integral operators.Conference on Prospects in Mathematics, Princeton University Press, 1971.
Hörmander, L.,Linear partial differential operators. Grundlehren d. Math. Wiss. 116. Springer-Verlag, 1963.
Keller, J. B., Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems.Ann. of Physics, 4 (1958), 180–188.
Kohn, J. J., &Nirenberg, L., On the algebra of pseudo-differential operators.Comm. Pure Appl. Math., 18 (1965), 269–305.
Kumano-go, H., Remarks on pseudo-differential operatorsJ. Math. Soc. Japan, 21 (1969), 413–439.
Lax, P. D., Asymptotic solutions of oscillatory initial value problems.Duke Math. J., 24 (1957), 627–646.
Ludwig, D., Exact and asymptotic solutions of the Cauchy problem.Comm. Pure Appl. Math., 13 (1960), 473–508.
Maslov, V. P.,Theory of pertubations and asymptotic methods. Moskov. Gos. Univ., Moscow, 1965 (Russian).
Nirenberg, L., Pseudo-differential operators.Amer. Math. Soc. Symp. Pure Math., 16 (1970), 149–167.
Nirenberg, L. &Trèves, F., On local solvability of linear partial differential equations. Part I: Necessary conditions. Part II: Sufficient conditions.Comm. Pure Appl. Math., 23 (1970), 1–38 and 459–510.
Palais, R.,Seminar on the Atiyah-Singer index theorem. Annals of Mathematics Studies 57, 1965.
Sato, M., Hyperfunctions and partial differential equations.Conf. on Functional Analysis and Related Topics, Tokyo 1969 91–94.
Sternberg, S.,Lectures on differential geometry. Prentice Hall, 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hörmander, L. Fourier integral operators. I. Acta Math. 127, 79–183 (1971). https://doi.org/10.1007/BF02392052
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02392052