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Fourier Integral Operators. I

In: Mathematics Past and Present Fourier Integral Operators

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  • L. Hörmander

Abstract

Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value is rather limited in genuinely non-elliptic problems. In this paper we shall therefore discuss some more general classes of operators which are adapted to such applications. For these operators we shall develop a calculus which is almost as smooth as that of pseudo-differential operators. It also seems that one gains some more insight into the theory of pseudo-differential operators by considering them from the point of view of the wider classes of operators to be discussed here so we shall take the opportunity to include a short exposition.

Suggested Citation

  • L. Hörmander, 1994. "Fourier Integral Operators. I," Springer Books, in: Jochen Brüning & Victor W. Guillemin (ed.), Mathematics Past and Present Fourier Integral Operators, pages 23-127, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-03030-1_2
    DOI: 10.1007/978-3-662-03030-1_2
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