arXiv subjects

Shinichiro Itozaki

Publications and source records attributed to Shinichiro Itozaki.

2 recordsLinked to original sources

arXiv2012

Existence of wave operators with time-dependent modifiers for the Schödinger equations with long-range potentials on scattering manifolds

We construct time-dependent wave operators for Schrödinger equations with long-range potentials on a manifold $M$ with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space of the form $\mathbb{R} \times \partial M$, where $\partial M$ is the boundary of $M$ at infinity. We construct exact solutions to the Hamilton-Jacobi equation on the reference system $\mathbb{R} \times \partial M$, and prove the existence of the modified wave operators.

math.AP↗

arXiv2011

Scattering theory for Schrödinger equations on manifolds with asymptotically polynomially growing ends

We study a time-dependent scattering theory for Schrödinger operators on a manifold with asymptotically polynomially growing ends. We use the Mourre theory to show the spectral properties of self-adjoint second-order elliptic operators. We prove the existence and the asymptotic completeness of wave operators using the smooth perturbation theory of Kato. We also consider a two-space scattering with a simple reference system.

math.AP↗