Abstract
The purpose of this paper is to give applications of the operator theory developed in the first part (Acta Math., 127 (1971), 79–183).
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andersson, K. G., Propagation of analyticity of solutions of partial differential equations with constant coefficients. Ark. Mat., 8 (1970), 277 - 302.
Birhhoff, G. D., Dynamical systems. Amer. Math. Soc. Coll. Publ. 9, New York, 1927.
Bourbaxi, N., Espaces vectoriels topologiques. Paris, 1953-55.
Bjorken, J. D. and Drell, S., Relativistic quantum fields. Mc Graw-Hill, New York, 1965.
Courant, R. and Lax, P. D., The propagation of discontinuities in wave motion. Proc. Nat. Acad. Sci. USA, 42 (1956), 872 - 876.
Dewitt, B. S., Dynamical theory of groups and fields. Relativity, groups and topology, 585-820. Gordon and Breach, New York-London, 1964.
Dieudonne, J. and Sçhwartz, L., La dualité dans les espaces (1) et (Cg). Ann. Inst. Fourier (Grenoble), 1 (1949), 61 - 101.
Dugundji, J. and Antosiewicz, H. A., Parallelizable flows and Lyapunov‘s second method. Ann. of Math., 73 (1961), 543 - 555.
Girding, L., Kotaxe, T. and 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.
Gruéin, V. V., The extension of smoothness of solutions of differential equations of principal type. Dokl. Akad. Nauk SSSR, 148 (1963), 1241-1244. Also in Soviet Math. Dokl., 4 (1963), 248 - 252.
Hadamard, J., Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques. Hermann, Paris 1932.
Haefliger, A., Variétés feuilletées. Ann. Scuola Norm. Sup. Pisa, 16 (1962), 367 - 397.
Hörmander, L., Introduction to complex analysis in several variables. D. van Nostrand Publ. Co., Princeton, N. J. 1965.
Hörmander, L., Pseudo-differential operators and non-elliptic boundary problems. Ann. of Math., 83 (1966), 129 - 209.
Hörmander, L., On the singularities of solutions of partial differential equations. Comm. Pure Appl. Math., 23 (1970), 329 - 358.
Hörmander, L.,Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients. Comm. Pure Appl. Math., 24 (1971), 671 - 704.
Hörmander, L., Linear differential operators. Actes Congr. Intern. Math. Nice, 1970, 1, 121 - 133.
Hörmander, L., On the existence and the regularity of solutions of linear pseudo-differential equations. L‘Enseignement Math., 17 (1971), 99 - 163.
Palais, R., A global formulation of the Lie theory of transformation groups. Mem. Amer. Math. Soc., 22 (1957).
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.
Riesz, M., L‘intégrale de Riemann-Liouville et le problème de Cauchy. Acta Math., 81 (1949), 1 - 223.
Steenrod, N., The topology of fiber bundles. Princeton Univ. Press, Princeton 1951.
Unterberger, A. and Bokobza, J., Les opérateurs pseudo-différentiels d‘ordre variable. C. R. Acad. Sci. Paris, 261 (1965), 2271 - 2273.
Whitney, H., Regular families of curves. Ann. of Math., 34 (1933), 244 - 270.
Zerner, M., Solutions singulières d‘équations aux dérivées partielles. Bull. Soc. Math. France, 91 (1963), 203 - 226.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Duistermaat, J.J., Hörmander, L. (1994). Fourier Integral Operators. II. In: Brüning, J., Guillemin, V.W. (eds) Mathematics Past and Present Fourier Integral Operators. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03030-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-03030-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08159-0
Online ISBN: 978-3-662-03030-1
eBook Packages: Springer Book Archive