Related papers: Gabor wave packets and evolution operators

In this paper we study the Cauchy problem for the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups when the time-dependent non-negative propagation speed is regular, H\"older, and distributional. For…

The paper is devoted to the problem of existence of propagators for an abstract linear non-autonomous evolution Cauchy problem of hyperbolic type in separable Banach spaces. The problem is solved using the so-called evolution semigroup…

In this paper, a family of random Jacobi matrices, with off-diagonal terms that exhibit power-law growth, is studied. Since the growth of the randomness is slower than that of these terms, it is possible to use methods applied in the study…

In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…

We use the method of group contractions to relate wavelets analysis and Gabor analysis. Wavelets analysis is associated with unitary irreducible representations of the affine group while Gabor analysis is associated with unitary irreducible…

We consider Scr\"odinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may be not even differentiable. The well-posedness of the Cauchy problem is proved in the frame of…

Hyperbolic transport-reaction equations are abundant in the description of movement of motile organisms. Here, we focus on system of four coupled transport-reaction equations that arises from an age-structuring of a species of turning…

In this paper, we characterized resonant interaction of weakly nonlinear hyperbolic waves in gas dynamics with a real gas background. An asymptotic approach is used to study the interaction between waves, governed by the Euler equations of…

We analyze energy decay for deep convolutional neural networks employed as feature extractors, including Mallat's wavelet scattering transform. For time-frequency scattering transforms based on Gabor filters, previous work has established…

Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…

We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…

We consider the Schr\"odinger equation \begin{equation*} i \displaystyle\frac{\partial u}{\partial t} +Hu=0,\quad H=a(x,D), \end{equation*} where the Hamiltonian $a(z)$, $z=(x,\xi)$, is assumed real-valued and smooth, with bounded…

We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…

In this note we give an elementary proof of the space-like real analyticity of solutions to a degenerate evolution problem that arises in the study of fractional parabolic operators of the type $(\partial_t - div_x(B(x)\nabla_x))^s$,…

We introduce a compact operator-based technique that solves the paraxial wave equation for a broad class of structured light fields. Using the spatial evolution operator to propagate two families of physically apodized inputs, Gaussian…

We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…

We study the regularity of weak solutions to evolution equations with distributed order fractional time derivative. We prove a weak Harnack inequality for nonnegative weak supersolutions and H\"older continuity of weak solutions to this…

Dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients are considered. The global time decay estimates of $L^p-L^q$ norms of propagators are obtained, and…

We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schr\"odinger type. The Hamiltonian is assumed to have a real-valued principal symbol with the anisotropic homogeneity…

In this paper, persistence properties of solutions are investigated for a 4-parameter family ($k-abc$ equation) of evolution equations having $(k+1)$-degree non-linearities and containing as its integrable members the Camassa-Holm, the…