Multiple semiclassical states for singular magnetic nonlinear Schrödinger equations.
Multiple tunnelings in d-dimensions : a quantum particle in a hierarchical potential
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates
Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality of order...
Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II
Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators
Nodal domain theorems à la Courant.
Nodal domains and spectral minimal partitions
Non hypoellipticité d'opérateurs elliptiques singuliers
Non-existence of wave operators for Stark effect Hamiltonians.
Norm group convergence for singular Schrödinger operators
Note to the paper by R. Hempel, A. M. Hinz, and H. Kalf: On the Essential Spectrum of Schrödinger Operators with Spherically Symmetric Potentials.
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.