A Lie group structure for pseudodifferential operators
The work consists of five sections. Section 1 is introductory. In section 2 the spaces of formal pseudodifferential operators and Fourier integral operators on a compact manifold M are described. In section 3 the basic facts on ILH (inverse limit Hilbert) Lie groups are reviewed and the ILH group structure for \(D_{\theta}(T^*M\setminus 0)\) are constructed, where \(D_{\theta}(T^*M\setminus 0)\) is the space of smooth diffeomorphisms of \(T^*M\setminus 0\) which preserve the canonical one- form \(\theta\) on \(T^*M\). In section 4 a global phase function for all \(\theta\)-preserving diffeomorphisms of \(T^*M\setminus 0\) which are \(C^ 1\)-close to the identity are constructed. This gives a global writing for invertible Fourier integral operators with canonical relation close to the identity. In section 5 the differentiable structure on invertible, order zero, formal pseudodifferential operators are introduced.
pseudodifferential and Fourier integral operators on manifolds
scientific article; zbMATH DE number 3942572
scientific article