Fourier Integral Operators. I

L. Hörmander

A chapter in Mathematics Past and Present Fourier Integral Operators, 1994, pp 23-127 from Springer

Abstract: 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.

Keywords: Line Bundle; Phase Function; Pseudodifferential Operator; Principal Symbol; Oscillatory Integral (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-3-662-03030-1_2

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