The theory of localized frames is refined to include quasi-Banach spaces and spaces with multiple generators. Applications are given to non-linear approximation with frames and to the convergence ofâ€¦ (More)

We study the composition of time-frequency localization operators (wavepacket operators) and develop a symbolic calculus of such operators on modulation spaces. The use of time-frequency methodsâ€¦ (More)

We study the dispersive properties of the SchrÃ¶dinger equation. Precisely, we look for estimates which give a control of the local regularity and decay at infinity separately. The Banach spaces thatâ€¦ (More)

We give a complete characterization of the continuity of pseudodif-ferential operators with symbols in modulation spaces M p,q , acting on a given Lebesgue space L r. Namely, we find the full rangeâ€¦ (More)

We deal with fixed-time and Strichartz estimates for the SchrÃ¶dinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some newâ€¦ (More)

We study localization operators within the framework of ultradistributions. More precisely, given a symbol a and two windows Ï†1, Ï†2, we investigate the multilinear mapping from (a, Ï†1, Ï†2) âˆˆ S â€²â€¦ (More)

We consider a class of Fourier integral operators, globally defined on R, with symbols and phases satisfying product type estimates (the so-called SG or scattering classes). We prove a sharpâ€¦ (More)

The objective of this paper is to report on recent progress on Strichartz estimates for the SchrÃ¶dinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgueâ€¦ (More)

We study the action of metaplectic operators on Wiener amalgam spaces, giving upper bounds for their norms. As an application, we obtain new fixed-time estimates in these spaces for SchrÃ¶dingerâ€¦ (More)

It is known that Fourier integral operators arising when solving SchrÃ¶dinger-type operators are bounded on the modulation spaces M p,q , for 1 â‰¤ p = q â‰¤ âˆž, provided their symbols belong to theâ€¦ (More)