Almost diagonalization theorem and global wave front sets in ultradifferentiable classes (Q6613297)

This paper deals with Weyl operators with symbol in ultradifferentiable classes with exponential weight. It establishes almost diagonalization theorems for these operators, both in the continuous and discrete cases. The paper then explores applications to the propagation of singularities, using a global wave front set defined by means of the short-time Fourier transform. Further interesting applications concern the invertibility and boundedness of pseudodifferential operators in modulation spaces with exponential growth.