Related papers: Misspecified Bernstein-Von Mises theorem for hiera…
We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain $D$ of ${\mathbb R}^n$ for a second order parameter-dependent elliptic differential operator $A (x,\partial, \lambda)$ with complex-valued essentially…
We derive new limit theorems for Brownian motion, which can be seen as non-exponential analogues of the large deviation theorems of Sanov and Schilder in their Laplace principle forms. As a first application, we obtain novel scaling limits…
The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and…
Many novel and unique physical phenomena of incommensurate systems can be illustrated and predicted using the spectra of the associated Schr\"odinger operators. However, the absence of periodicity in these systems poses significant…
This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…
We study semilinear non-local elliptic problems driven by spectral-type operators of the form $\psi(-L_{|D})$ in a bounded $C^{1,1}$ domain $D\subset \mathbb{R}^d$ with a nonhomogeneous boundary condition. Here $\psi$ is a Bernstein…
In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an…
We establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…
We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
We begin a study of a multi-parameter family of Cauchy initial-value problems for the modified nonlinear Schr\"odinger equation, analyzing the solution in the semiclassical limit. We use the inverse scattering transform for this equation,…
In this work we investigate a class of degenerate Schr\"odinger equations associated to degenerate elliptic operators with irregular potentials on $\Ran$ by introducing a suitable H\"ormander metric $g$ and a $g$-weight $m$. We establish…
For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…
We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a…
We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors and the optimal order of convergence and define suitable…
We propose an approach to nonlinear evolution equations with large and decaying external potentials that addresses the question of controlling globally-in-time the nonlinear interactions of localized waves in this setting. This problem…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
We study a class of focusing nonlinear Schroedinger-type equations derived recently by Dumas, Lannes and Szeftel within the mathematical description of high intensity laser beams [7]. These equations incorporate the possibility of a…
In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schr{\"o}dinger class with a combination of a focusing biharmonic operator with either an isotropic or…