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25 Years of Fourier Integral Operators

In: Mathematics Past and Present Fourier Integral Operators

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  • V. W. Guillemin

Abstract

I am grateful to Lars Hörmander and to my collaborator, Hans Duistermaat, for allowing us to reprint the two classical articles on Fourier integral operators: F.I.O., I (Acta Mathematica, Vol. 127, pp. 77–183) and II (Acta Mathematica, Vol. 128, pp. 184–269). Much of the material in these articles is now available in book form. In particular many would regard the definitive treatment of Fourier integral operators as being Volumes Ill and IV of Hörmander’s book [26]. Nevertheless I feel there are two very good reasons for going to the trouble of reprinting these articles as an ensemble. One is that they provide a relatively concise introduction to this subject. For someone who is trying to get a sense of the lay of the land they are probably a better place to start than Hörmander’s book or any other standard text book. Though these two papers (particularly F.I.O. I) would probably pose problems for someone who had never seen pseudodifferential operators before, they are essentially self-contained, and, considering the fact that they cover a lot of ground very quickly, are quite readable as well.

Suggested Citation

  • V. W. Guillemin, 1994. "25 Years of Fourier Integral Operators," Springer Books, in: Jochen Brüning & Victor W. Guillemin (ed.), Mathematics Past and Present Fourier Integral Operators, pages 1-21, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-03030-1_1
    DOI: 10.1007/978-3-662-03030-1_1
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