1,721,152 research outputs found
Sharp continuity results for the short-time Fourier transform and for localization operators
No full textSome new Strichartz estimates for the Schroedinger equation
No full textWe deal with fixed-time and Strichartz estimates for the Schrödinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones. As an application, we present a result on the wellposedness of the linear Schrödinger equation with a rough time-dependent potentia
Remarks on Fourier multipliers and applications to the Wave equation
No full textAbstractExploiting continuity properties of Fourier multipliers on modulation spaces and Wiener amalgam spaces, we study the Cauchy problem for the NLW equation. Local wellposedness for rough data in modulation spaces and Wiener amalgam spaces is shown. The results formulated in the framework of modulation spaces refine those in [A. Bényi, K.A. Okoudjou, Local well-posedness of nonlinear dispersive equations on modulation spaces, preprint, April 2007 (available at ArXiv:0704.0833v1)]. The same arguments may apply to obtain local wellposedness for the NLKG equation
Excursus on modulation spaces via metaplectic operators and related time-frequency representations
Full text linkWe provide a comprehensive overview of the theoretical framework surrounding modulation spaces and their characterizations, particularly focusing on the role of metaplectic operators and time-frequency representations. We highlight the metaplectic action which is hidden in their construction and guarantees equivalent (quasi-)norms for such spaces. In particular, this work provides new characterizations via the sub- manifold of shift-invertible symplectic matrices. Similar results hold for the Wiener amalgam spaces
Kernel Theorems for Modulation Spaces
No full textWe deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces M p for every
1 ≤ p ≤ ∞, by the membership of its kernel in (mixed) modulation spaces. Whereas Feichtinger’s kernel theorem (which we recapture as a special case) is the modulation space counterpart of Schwartz’ kernel theorem for tempered distributions, our results do not have a counterpart in distribution theory. This reveals the superiority, in some respects, of the modulation space formalism over distribution theory, as already emphasized in Feichtinger’s manifesto for a post-modern harmonic analysis, tailored
to the needs of mathematical signal processing. The proof uses in an essential way a discretization of the problem by means of Gabor frames. We also show the equivalence of the operator norm and the modulation space norm of the corresponding kernel. For operators acting on M p,q a similar characterization is not expected, but sufficient conditions for boundedness can be stated in the same spiri
Metaplectic Gabor Frames of Wigner-Decomposable Distributions
No full textMetaplectic Wigner distributions generalize the most popular time-frequency representations, such as the short-time Fourier transform (STFT) and -Wigner distributions, using metaplectic operators. However, for a metaplectic Wigner distribution to measure the local time-frequency concentration of signals, the additional property of shift-invertibility is fundamental. In addition, metaplectic atoms provide different ways to model signals. Namely, signals can be written as discrete superpositions of these operators, providing original ways to represent signals, with applications to machine learning, signal analysis, theory of pseudodifferential operators, to mention a few. Among all shift-invertible distributions, Wigner-decomposable metaplectic Wigner distributions provide the most straightforward generalization of the STFT. In this work, we focus on metaplectic atoms of Wigner-decomposable shift-invertible metaplectic distributions and characterize the associated metaplectic Gabor frames
- …
