On regular Fréchet-Lie groups. VIII: Primordial operators and Fourier integral operators
In this paper, we prove that the group of invertible Fourier-integral operators of order 0 is a regular Fréchet-Lie group with the Lie algebra \(\sqrt{-1}{\mathcal P}^ 1\), where \({\mathcal P}^ 1\) is the totality of pseudo-differential operators of order one with the real principal symbols. As stated in the preface of \textit{H. Omori}, \textit{Y. Maeda} and \textit{A. Yoshioka}, ibid. 3, 353-390 (1980; Zbl 0461.58003), this is the main purpose of this series. So, this paper is the final one of our series.
group of invertible Fourier-integral operators of order 0
pseudo- differential operators of order one
scientific article; zbMATH DE number 3932065