Fourier integral operators. I

Lars Hörmander

doi:10.1007/bf02392052

journal article Jan 01, 1971

Fourier integral operators. I

Lars Hörmander

Acta Mathematica Vol. 127 pp. 79-183 · International Press of Boston

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References

28

[1]

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. 10.1007/bf01075861

[2]

Atiyah, M. F.,K-theory. Benjamin 1968.

[3]

Atiyah, M. F. &Bott, R., A Lefschetz fixed point formula, for elliptic complexes I.Ann. of Math., 86 (1967), 374–407. 10.2307/1970694

[4]

Opérateurs pseudo-différentiels sur une variété différentiable

Juliane Bokobza-Haggiag

Annales de l'Institut Fourier 1969 10.5802/aif.311

[5]

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.

[6]

Carathéodory, C.,Variationsrechnung und partielle Differentialgleichungen Erster Ordnung. Teubner, Berlin, 1935.

[7]

Egorov, Yu. V., On canonical transformations of pseudo-differential operators.Uspehi Mat. Nauk. 25 (1969), 235–236.

[8]

—, On non-degenerate hypoelliptic pseudo-differential operators.Doklady Akad. Nauk SSSR. 186 (1969), 1006–1007. (Russian.) English translationSoviet Math. Doklady, 10 (1969), 697–699.

[9]

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.

[10]

Friedrichs, K.,Pseudo-differential operators. An introduction. Lecture notes, Courant Institute, New York University 1968.

[11]

Hirzebruch, P.,Topological methods in algebraic geometry. Grundlehren der Math. Wiss. 131, Springer-Verlag 1966. 10.1007/978-3-642-62018-8

[12]

Hörmander, L., Pseudo-differential operators,Comm. Pure Appl. Math., 18 (1965), 501–517. 10.1002/cpa.3160180307

[13]

—, Pseudo-differential operators and hypoelliptic equations.Amer. Math. Soc. Symp. Pure Math., 10 (1966), Singular integral operators, 138–183. 10.1090/pspum/010/0383152

[14]

—, The spectral function of an elliptic operator.Acta Math., 121 (1968) 193–218. 10.1007/bf02391913

[15]

Hörmander, L., On the singularities of solutions of partial differential equations.Conf. on Funct. Anal. and Related Topics, Tokyo 1969, 31–40.

[16]

Hörmander, L., The calculus of Fourier integral operators.Conference on Prospects in Mathematics, Princeton University Press, 1971. 10.1515/9781400881697-003

[17]

Hörmander, L.,Linear partial differential operators. Grundlehren d. Math. Wiss. 116. Springer-Verlag, 1963. 10.1007/978-3-642-46175-0

[18]

Keller, J. B., Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems.Ann. of Physics, 4 (1958), 180–188. 10.1016/0003-4916(58)90032-0

[19]

Kohn, J. J., &Nirenberg, L., On the algebra of pseudo-differential operators.Comm. Pure Appl. Math., 18 (1965), 269–305. 10.1002/cpa.3160180121

[20]

Kumano-go, H., Remarks on pseudo-differential operatorsJ. Math. Soc. Japan, 21 (1969), 413–439. 10.2969/jmsj/02130413

[21]

Lax, P. D., Asymptotic solutions of oscillatory initial value problems.Duke Math. J., 24 (1957), 627–646. 10.1215/s0012-7094-57-02471-7

[22]

Exact and asymptotic solutions of the cauchy problem

Donald Ludwig

Communications on Pure and Applied Mathematics 1960 10.1002/cpa.3160130310

[23]

Maslov, V. P.,Theory of pertubations and asymptotic methods. Moskov. Gos. Univ., Moscow, 1965 (Russian).

[24]

Nirenberg, L., Pseudo-differential operators.Amer. Math. Soc. Symp. Pure Math., 16 (1970), 149–167. 10.1090/pspum/016/0270217

[25]

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. 10.1002/cpa.3160230102

[26]

Palais, R.,Seminar on the Atiyah-Singer index theorem. Annals of Mathematics Studies 57, 1965. 10.1515/9781400882045

[27]

Sato, M., Hyperfunctions and partial differential equations.Conf. on Functional Analysis and Related Topics, Tokyo 1969 91–94.

[28]

Sternberg, S.,Lectures on differential geometry. Prentice Hall, 1965.

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