×

zbMATH — the first resource for mathematics

Fourier integral operators. I. (English) Zbl 0212.46601

MSC:
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
47G10 Integral operators
35S30 Fourier integral operators applied to PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
47G30 Pseudodifferential operators
PDF BibTeX XML Cite
Full Text: DOI
References:
[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. · doi: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. · Zbl 0161.43201 · doi:10.2307/1970694
[4] Bokobza-Haggiag, J., Opérateurs pseudo-différentiels sur une variété différentiable.Ann. Inst. Fourier, Grenoble, 19 (1969), 125–177. · Zbl 0176.08702
[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. · Zbl 0204.44805
[6] Carathéodory, C.,Variationsrechnung und partielle Differentialgleichungen Erster Ordnung. Teubner, Berlin, 1935. · JFM 61.0547.01
[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. · Zbl 0138.42001
[12] Hörmander, L., Pseudo-differential operators,Comm. Pure Appl. Math., 18 (1965), 501–517. · Zbl 0125.33401 · doi:10.1002/cpa.3160180307
[13] –, Pseudo-differential operators and hypoelliptic equations.Amer. Math. Soc. Symp. Pure Math., 10 (1966), Singular integral operators, 138–183.
[14] –, The spectral function of an elliptic operator.Acta Math., 121 (1968) 193–218. · Zbl 0164.13201 · doi: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. · Zbl 0235.47023
[17] Hörmander, L.,Linear partial differential operators. Grundlehren d. Math. Wiss. 116. Springer-Verlag, 1963.
[18] Keller, J. B., Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems.Ann. of Physics, 4 (1958), 180–188. · Zbl 0085.43103 · doi: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. · Zbl 0171.35101 · doi:10.1002/cpa.3160180121
[20] Kumano-go, H., Remarks on pseudo-differential operatorsJ. Math. Soc. Japan, 21 (1969), 413–439. · Zbl 0179.42201 · doi:10.2969/jmsj/02130413
[21] Lax, P. D., Asymptotic solutions of oscillatory initial value problems.Duke Math. J., 24 (1957), 627–646. · Zbl 0083.31801 · doi:10.1215/S0012-7094-57-02471-7
[22] Ludwig, D., Exact and asymptotic solutions of the Cauchy problem.Comm. Pure Appl. Math., 13 (1960), 473–508. · Zbl 0098.29601 · doi: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. · Zbl 0218.35075
[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. · Zbl 0191.39103 · doi:10.1002/cpa.3160230102
[26] Palais, R.,Seminar on the Atiyah-Singer index theorem. Annals of Mathematics Studies 57, 1965. · Zbl 0137.17002
[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. · Zbl 0129.13102
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.