Related papers: On the Strichartz estimates for orthonormal system…
We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the…
We investigate dispersive and Strichartz estimates for the Schr\"{o}dinger time evolution propagator $\mathrm{e}^{-\mathrm{i}tH}$ on a star-shaped metric graph. The linear operator, $H$, taken into consideration is the self-adjoint…
In this paper we obtain some new Strichartz estimates for the wave propagator $e^{it\sqrt{-\Delta}}$ in the context of Wiener amalgam spaces. While it is well understood for the Schr\"odinger case, nothing is known about the wave…
In this article, we study the scattering theory for the two dimensional defocusing quintic nonlinear Schr\"odinger equation(NLS) with partial harmonic oscillator which is given by \begin{align}\label{NLS-abstract} \begin{cases}\tag{PHNLS}…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
The present paper is devoted to the semiclassical analysis of linear Schr\"odinger equations from a Gabor frame perspective. We consider (time-dependent) smooth Hamiltonians with at most quadratic growth. Then we construct higher order…
We prove an explicit weighted estimate for the semiclassical Schr\"odinger operator $P = - h^2 \partial^2_x + V(x;h)$ on $L^2(\mathbb{R})$, with $V(x;h)$ a finite signed measure, and where $h >0$ is the semiclassical parameter. The proof is…
We consider the nonlinear Schr\"odinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class $W^{\alpha,2}$ for some $\alpha\in (0,1)$. Due to the loss of…
In this paper, we studied the space-time estimates for the solution to the Schr\"odinger equation. By polynomial partitioning, induction arguments, bilinear to linear arguments and broad norm estimates, we set up several maximal estimates…
Let $L=-\Delta + V(x)$ be a Schr\"odinger operator on $\mathbb R^d$, where $V(x)\geq 0$, $V\in L^2_{\rm loc} (\mathbb R^d)$. We give a short proof of dimension free $L^p(\mathbb R^d)$ estimates, $1<p\leq 2$, for the vector of the Riesz…
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…
The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schr\"{o}dinger equation at low regularity. Its temporal convergence was recently analyzed in a framework of discrete…
Concerned with elliptic operators with stationary random coefficients of integrable correlations and bounded Lipschitz domains, arising from stochastic homogenization theory, this paper is mainly devoted to studying Calder\'on-Zygmund…
In this article we reconsider the problem of the propagation of waves in a random medium in a kinetic regime. The final aim of this program would be the understanding of the conditions which allow to derive a kinetic or radiative transfer…
In \cite{PRA} and \cite{SSM} the orthonormal Strichartz estimates for the Schr\"odinger equation associated with the Dunkl Laplacian and the Dunkl-Hermite operator are obtained. In this article, we prove a necessary condition on the…
We consider time dependent harmonic oscillators and construct a parametrix to the corresponding Schr\"odinger equation using Gaussian wavepackets. This parametrix of Gaussian wavepackets is precise and tractable. Using this parametrix we…
This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…
This paper is dedicated to studying pointwise estimates of the fundamental solution for the higher order Schr\"{o}dinger equation: % we investigate the fundamental solution of the higher order Schr\"{o}dinger equation…
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $\mathbb R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all…
In this paper we study weighted estimates for the multi-frequency $\omega-$Calder\'{o}n-Zygmund operators $T$ associated with the frequency set $\Theta=\{\xi_1,\xi_2,\dots,\xi_N\}$ and modulus of continuity $\omega$ satisfying the usual…