Lie Groups of Fourier Integral Operators on Open Manifolds

Lie Groups of Fourier Integral Operators on Open Manifolds

We endow the group of invertible Fourier integral operators on an open manifold with the structure of an ILH Lie group. This is done by establishing such structures for the groups of invertible pseudodifferential operators and contact transformations on an open manifold of bounded geometry, and gluing those together via a local section.

The Lie Group of Fourier Integral Operators on Open Manifolds

The theory of pseudodifferential operators and Fourier integral operators on compact manifolds is well established and their applications in mathematical physics well known , see for example Hörmander , Duistermaat , Treves 12 . For open (non compact) manifolds this is not the case, and that’s what I would like to focus on in this paper. We are interested in the geometry of the spaces of pseudo...

ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

Semi-Classical Wavefront Set and Fourier Integral Operators

Here we define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators and prove a generalization of Egorov’s Theorem to manifolds of different dimensions.

Fourier Integral Operators and Harmonic Analysis On Compact Manifolds