Related papers: Optimal estimates for the double dispersion operat…
We are concerned with the inverse scattering problem for the full line Schr\"odinger operator $-\partial_x^2+q(x)$ with a steplike potential $q$ a priori known on $\Reals_+=(0,\infty)$. Assuming $q|_{\Reals_+}$ is known and short range, we…
We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective…
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…
We prove that the eigenvalues of a continuum random Schr\"odinger operator $-\Delta+ V_{\omega}$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all…
We consider the problem of recovering a smooth, compactly supported potential on R^3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…
We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.
We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schr\"odinger operator can be recovered H\"older stably from the boundary spectral data. This…
We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse the nonlinear inverse problem…
The regularity of integration kernels forces decay rates of singular values of associated integral operators. This is well-known for symmetric operators with kernels defined on $(a,b) \times (a,b)$, where $(a,b)$ is an interval. Over time,…
Direct and inverse scattering problem for an operator with non-local potential is solved in the paper. The method is based on the Riemann boundary value problem on a bundle of three straight lines. Description of scattering problem data is…
In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…
Fully-nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A new formulation of the optimization is…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
Latent class models are widely used for identifying unobserved subgroups from multivariate categorical data in social sciences, with binary data as a particularly popular example. However, accurately recovering individual latent class…
We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…
In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau…
Integral equations for meson-baryon scattering amplitudes are obtained by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of baryon chiral perturbation theory. Effective potentials are defined as…
The elastic neutron-${}^3\mathrm{H}$ scattering at intermediate energies is studied using rigorous integral equations solved in the momentum-space partial-wave basis. The four-particle transition operators are expanded into…
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…