Year: 2010
Type: article
Abstract: Time-frequency methods are used to study a class of Fourier IntegralOperators (FIOs) whose representation using Gabor frames is provedto be very efficient. Indeed, similarly to the case of shearlets and curveletsframes [10, 35], the matrix representation of a Fourier Integral Operator withrespect to a Gabor frame is well-organized. This is used as a powerful toolto study the boundedness of FIOs on modulation spaces. As special cases,we recapture boundedness results on modulation spaces for pseudo-differentialoperators with symbols in $M^{\infty, 1}$ [33], for some Fourier multipliers [6] andmetaplectic operators [14, 31]. Moreover, this paper provides the mathematicaltools to numerically solving the Cauchy problem for Schr¨odinger equationsusing Gabor frames [17]. Finally, similar arguments can be employed to studyother classes of FIOs [16].
Authors: Elena Cordero, Fabio Nicola, Luigi Rodino
Institution: University of Turin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2017485451