Obere Schranken für Eigenfunktionen eines Operators - ... + q.
Oč vlastně jde v teorii Schrodingerových operátorů?
On a class of non linear Schrödinger equations. III. Special theories in dimensions 1, 2 and 3
On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes
This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the normal derivative of the groundstate on the boundary. We then propose to use this formulation in the...
On an initial-boundary value problem for the nonlinear Schrödinger equation.
On approximation of solutions to some -dimensional integrable systems by Bäcklund transformations.
On Bernoulli decomposition of random variables and recent various applications
In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.
On Dirichlet-Schrödinger operators with strong potentials
We consider Schrödinger operators H = -Δ/2 + V (V≥0 and locally bounded) with Dirichlet boundary conditions, on any open and connected subdomain which either is bounded or satisfies the condition as |x| → ∞. We prove exponential decay at the boundary of all the eigenfunctions of H whenever V diverges sufficiently fast at the boundary ∂D, in the sense that as . We also prove bounds from above and below for Tr(exp[-tH]), and in particular we give criterions for the finiteness of such trace....
On elliptic systems pertaining to the Schrödinger equation
We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.
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.