Resolvent estimates for the magnetic Schrödinger operator

Resolvent Estimates of the Dirac Operator

Semiclassical resolvent estimates for Schrödinger operators with Coulomb singularities

Consider the Schrödinger operator with semiclassical parameter h, in the limit where h goes to zero. When the involved long-range potential is smooth, it is well known that the boundary values of the operator’s resolvent at a positive energy λ are bounded by O(h−1) if and only if the associated Hamilton flow is non-trapping at energy λ. In the present paper, we extend this result to the case wh...

Edge currents and eigenvalue estimates for magnetic barrier Schrödinger operators

We study two-dimensional magnetic Schrödinger operators with a magnetic field that is equal to b > 0 for x > 0 and −b for x < 0. This magnetic Schrödinger operator exhibits a magnetic barrier at x = 0. The unperturbed system is invariant with respect to translations in the ydirection. As a result, the Schrödinger operator admits a direct integral decomposition. We analyze the band functions of ...

Resolvent Operator Method for General Variational Inclusions

In this paper, we introduce a new class of variational inclusions involving three operator. Using the resolvent operator technique, we establish the equivalence between the general variational inclusions and the resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving the general variational inclusions. We also consider the cr...

Semiclassical Resolvent Estimates for Trapping Perturbations

We study the semiclassical estimates of the resolvent R(+ ii); 2 J R + ; 2]0;1] of a self-adjoint operator L(h) in the space of bounded operators L(H 0;s ; H 0;?s); s > 1=2. In the general case of long-range trapping "black-box" perturbations we prove that the estimate of the cut-oo resolvent k(x)R(+i0)(x)k H!H C exp(Ch ?p); (x) 2 C 1 0 (R n); p 1 implies the estimate kR(+ ii)k s;?s C 1 exp(C 1...