The study of Schrödinger operators within the framework of functional analysis has led to significant advances in our understanding of differential operators and their associated function spaces. In ...

Dispersive estimates for Schrödinger operators lie at the heart of contemporary analysis in quantum mechanics and partial differential equations. These estimates characterise the decay of solutions ...

Journal of Operator Theory, Vol. 70, No. 1 (Summer 2013), pp. 109-144 (36 pages) We present a variant of Mourre's commutator theory. We apply it to prove the limiting absorption principle for ...

Let G be a nilpotent Lie groups equipped with a Hörmander system of vector fields X = (X₁..., Xm) and $\Delta = \Sigma _{i = 1}^mX_i^2$ be the sub-Laplacians associated with X. Let A = — + W be the ...

It is well known that the resolvent at energy m>0 of the free Schrödinger operator on weighted L^2 spaces has norm decaying like m^{-1/2}. We show that this result is still valid for first-order ...