On Essential Self-Adjointness for Singular Elliptic Differential Operators.
On existence and nonexistence results for nonlinear Schrödinger equations
On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum
On factorization of Fefferman's inequality
On Non-Degeneracy of the Ground State of Schrödinger Operators.
On non-overdetermined inverse scattering at zero energy in three dimensions
We develop the -approach to inverse scattering at zero energy in dimensions of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction of the Faddeev generalized scattering amplitude in the...
On nonperturbative localization with quasi-periodic potential.
On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case
We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.
On some new spectral estimates for Schrödinger-like operators
We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with matrix-valued potentials and Sobolev inequalities for warped product spaces.
On some Schrödinger operators with a singular complex potential
On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator H... W in a spectral gap of H.
On the asymptotics of scattering phases for the Schrödinger equation
On the Bethe-Sommerfeld conjecture
We consider the operator in , of the form with a function periodic with respect to a lattice in . We prove that the number of gaps in the spectrum of is finite if . Previously the finiteness of the number of gaps was known for . Various approaches to this problem are discussed.
On the decay of the solutions of some nonlinear Schrödinger equations
On the density of the range for some nonlinear operators
On the Dirichlet problem associated with the Dunkl Laplacian
This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian as well as the hypoellipticity of on noninvariant open sets.
On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback
We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability...
On the eigenvalue asymptotics of certain Schrödinger operators
Subelliptic estimates on nilpotent Lie groups and the Cwikel-Lieb-Rosenblum inequality are used to estimate the number of eigenvalues for Schrödinger operators with polynomial potentials.
On the equivalence of Green functions for general Schrödinger operators on a half-space
We consider the general Schrödinger operator on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity considered by Zhao and Pinchover. As an application we study the cone of all positive L-solutions continuously vanishing...
On the essential spectrum and eigenvalue asymptotics of certain Schrödinger operators