Related papers: Dispersive estimates for Dirac Operators in dimens…
We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in…
In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the…
In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…
We study the spectrum of two kinds of operators involving a conical geometry: the Dirichlet Laplacian in conical layers and Schr\"odinger operators with attractive $\delta$-interactions supported by infinite cones. Under the assumption that…
This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of…
We establish resolvent estimates that extend earlier results to a larger class of electric potentials $V\in L^\infty(\mathbb{R}^d;\mathbb{R})$, $d\ge 3$, and magnetic potentials $b\in L^\infty(\mathbb{R}^d;\mathbb{R}^d)$ such that $V(x),…
This paper is devoted to studying time decay estimates of the solution for Beam equation (higher order type wave equation) with a potential $$u_{t t}+\big(\Delta^2+V\big)u=0, \,\ u(0, x)=f(x),\ u_{t}(0, x)=g(x)$$ in dimension three, where…
We study a complex perturbation of a self-adjoint infinite band Schrodinger operator (defined in the form sense), and obtain the Lieb--Thirring type inequalities for the rate of convergence of the discrete spectrum of the perturbed operator…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to study a family of…
In dimension $d\geq 3$, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schr\"odinger operators have no resonances. If $d=2$, we show that there are potentials with no resonances away…
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…
We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are…
We prove the absence of eigenvaues of the three-dimensional Dirac operator with non-Hermitian potentials in unbounded regions of the complex plane under smallness conditions on the potentials in Lebesgue spaces. Our sufficient conditions…
In this paper we study spectral properties associated to Schrodinger operator with potential that is an exponential decaying function. As applications we prove local energy decay for solutions to the perturbed wave equation and lack of…
We study time decay estimates of the fourth-order Schr\"{o}dinger operator $H=(-\Delta)^{2}+V(x)$ in $\mathbb{R}^{d}$ for $d=3$ and $d\geq5$. We analyze the low energy and high energy behaviour of resolvent $R(H; z)$, and then derive the…
We consider self-adjoint extensions of differential operators of the type $ (-\frac{d^2}{dr^2} + \frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2 with two kinds of boundary conditions: first that nullify the value of a function and…
We first prove semiclassical resolvent estimates for the Schr{\"o}dinger operator in R d , d $\ge$ 3, with real-valued potentials which are H{\"o}lder with respect to the radial variable. Then we extend these resolvent estimates to exterior…
Random Schroedinger operators with imaginary vector potentials are studied in dimension one. These operators are non-Hermitian and their spectra lie in the complex plane. We consider the eigenvalue problem on finite intervals of length n…
Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and…