We consider scattering theory for a pair of operators and on<br /> , where is a Riemannian manifold, is a multiplication<br />
operator on and is a pseudodifferential operator of order ,<br />
$\mu...
We consider the scattering theory for discrete Schr\"odinger operators on<br /> with long-range potentials. We prove the existence of modified wave<br />
operators constructed in terms of solutions of a Hamilton-Jacobi equation on<br />...
In a previous paper by the second author, we discussed a characterization of<br />
the microlocal singularities for solutions to Schr\"odinger equations with long<br />
range type perturbations, using solutions to a Hamilton-Jacobi equation. ...
Transactions of the American Mathematical Society 366(4) 1725-1747 2014年
The object of study in this paper is the on-shell scattering matrix S(E) of the Schrodinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of S(E) in the semiclassical limit when...
On this short note, we apply the Mourre theory of the limiting absorption<br />
with {\it difference} type conditions on the potential, instead of conditions<br />
on the derivatives. In order that we modify the definition of the conjugate<br />
o...
人文科学研究科
理学部