On Regular Fréchet-Lie Group of Invertible Inhomogeneous Fourier Integral Operators on $\mathbf{R}^n$

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...

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.

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 pseudodiierential 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 * and Applications to Fluid Dynamics

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.