Fourier integral operators. I

1971/01/01 by Lars Hörmander · 15 citations
Engineering · Computer Science · Mathematics · #Physics and Engineering Research Articles #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis

paper · pdf · doi:10.1007/bf02392052

openalex publication_date 1971/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Citations

• Asymptotic solutions of oscillatory initial value problems
• The spectral function of an elliptic operator
• Characteristic class entering in quantization conditions

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