Zobrazeno 1 - 10
of 131
pro vyhledávání: '"Trapasso, S."'
Autor:
Trapasso, S. Ivan
We perform a phase space analysis of evolution equations associated with the Weyl quantization $q^{\mathrm{w}}$ of a complex quadratic form $q$ on $\mathbb{R}^{2d}$ with non-positive real part. In particular, we obtain pointwise bounds for the matrix
Externí odkaz:
http://arxiv.org/abs/2408.11130
We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave packets)
Externí odkaz:
http://arxiv.org/abs/2407.15521
The full characterization of the class of Fresnel integrable functions is an open problem in functional analysis, with significant applications to mathematical physics (Feynman path integrals) and the analysis of the Schr\"odinger equation. In finite
Externí odkaz:
http://arxiv.org/abs/2403.20082
Autor:
Trapasso, S. Ivan
We prove boundedness results on modulation and Wiener amalgam spaces for some families of spectral multipliers for the twisted Laplacian. We exploit the metaplectic equivalence relating the twisted Laplacian with a partial harmonic oscillator, leadin
Externí odkaz:
http://arxiv.org/abs/2306.00592
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear measureme
Externí odkaz:
http://arxiv.org/abs/2302.03577
We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator $e^{-tH^{\beta}}$, $t, \beta>0$, associated with the harmonic oscillator $H=-\Delta + |x|^2$. We then prove some local and global wellposedness results
Externí odkaz:
http://arxiv.org/abs/2210.07691
Autor:
Nicola, Fabio, Trapasso, S. Ivan
Within the mathematical analysis of deep convolutional neural networks, the wavelet scattering transform introduced by St\'ephane Mallat is a unique example of how the ideas of multiscale analysis can be combined with a cascade of modulus nonlinearit
Externí odkaz:
http://arxiv.org/abs/2205.11142
We consider the problem of the maximum concentration in a fixed measurable subset $\Omega\subset\mathbb{R}^{2d}$ of the time-frequency space for functions $f\in L^2(\mathbb{R}^{d})$. The notion of concentration can be made mathematically precise by c
Externí odkaz:
http://arxiv.org/abs/2112.09675
Autor:
Trapasso, S. Ivan
In this note we study the properties of a sequence of approximate propagators for the Schr\"odinger equation, in the spirit of Feynman's path integrals. Precisely, we consider Hamiltonian operators arising as the Weyl quantization of a quadratic form
Externí odkaz:
http://arxiv.org/abs/2107.00886
Autor:
Nicola, Fabio, Trapasso, S. Ivan
The problem of robustness under location deformations for deep convolutional neural networks (DCNNs) is of great theoretical and practical interest. This issue has been studied in pioneering works, especially for scattering-type architectures, for de
Externí odkaz:
http://arxiv.org/abs/2104.11977