Year: 2012
Type: preprint
Abstract: We perform a time-frequency analysis of Fourier multipliers and, more generally, pseudodifferential operators with symbols of Gevrey, analytic and ultra-analytic regularity. As an application we show that Gabor frames, which provide optimally sparse decompositions for Schroedinger-type propagators, reveal to be an even more efficient tool for representing solutions to a wide class of evolution operators with constant coefficients, including weakly hyperbolic and parabolic-type operators. Besides the class of operators, the main novelty of the paper is the proof of super-exponential (as opposite to super-polynomial) off-diagonal decay for the Gabor matrix representation.
Source: arXiv (Cornell University)
Authors: Cordero, Elena, Nicola, Fabio, Rodino, Luigi
Institutions: University of Turin, Politecnico di Torino
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952938347