Fourier integral operators. I

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.

Locations

• Acta Mathematica - View - PDF