Zobrazeno 1 - 10
of 793
pro vyhledávání: '"A Giacchi"'
The integration of operator kernels with the Wigner distribution, first conceptualized by E. Wigner in 1932 and later extended by L. Cohen and others, has opened new avenues in time-frequency analysis and operator calculus. Despite substantial advanc
Externí odkaz:
http://arxiv.org/abs/2412.01960
Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in $L^2(\mathbb{R}^d)$ and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to the propagat
Externí odkaz:
http://arxiv.org/abs/2410.13818
Autor:
Giacchi, Gianluca, Iakovidis, Isidoros, Milani, Bastien, Stuber, Matthias, Murray, Micah, Franceschiello, Benedetta
Magnetic Resonance Imaging (MRI) is a powerful technique employed for non-invasive in vivo visualization of internal structures. Sparsity is often deployed to accelerate the signal acquisition or overcome the presence of motion artifacts, improving t
Externí odkaz:
http://arxiv.org/abs/2406.19239
In this work, we extend Wigner's original framework to analyze linear operators by examining the relationship between their Wigner and Schwartz kernels. Our approach includes the introduction of (quasi-)algebras of Fourier integral operators (FIOs),
Externí odkaz:
http://arxiv.org/abs/2405.16448
Autor:
Giacchi, Gianluca
Housdorff-Young's inequality establishes the boundedness of the Fourier transform from $L^p$ to $L^q$ spaces for $1\leq p\leq2$ and $q=p'$, where $p'$ denotes the Lebesgue-conjugate exponent of $p$. This paper extends this classical result by charact
Externí odkaz:
http://arxiv.org/abs/2405.09378
We exhibit the connection between the Wigner kernel and the Gabor matrix of a linear bounded operator T : $\mathcal{S}(\mathbb{R}^d) \to \mathcal{S}' (\mathbb{R}^d)$. The smoothing effect of the Gabor matrix is highlighted by basic examples. This con
Externí odkaz:
http://arxiv.org/abs/2404.08332
We study the decay properties of Wigner kernels for Fourier integral operators of types I and II. The symbol spaces that allow a nice decay of these kernels are the Shubin classes $\Gamma^m(\mathbb{R^{2d}})$, with negative order $m$. The phases consi
Externí odkaz:
http://arxiv.org/abs/2402.02809
To overcome the impossibility of representing the energy of a signal simultaneously in time and frequency, many time-frequency representations have been introduced in the literature. Some of these are recalled in the Introduction. In this work we pro
Externí odkaz:
http://arxiv.org/abs/2401.03882
We perform a Wigner analysis of Fourier integral operators (FIOs), whose main examples are Schr\"odinger propagators arising from quadratic Hamiltonians with bounded perturbations. The perturbation is given by a pseudodifferential operator $\sigma(x,
Externí odkaz:
http://arxiv.org/abs/2311.18383
Autor:
Cordero, Elena, Giacchi, Gianluca
Modulation spaces were originally introduced by Feichtinger in 1983. Since the 2000s there have been thousands of contributions using them as correct framework; they range from PDEs, pseudodifferential operators, quantum mechanics, signal analysis. T
Externí odkaz:
http://arxiv.org/abs/2305.13166