arXiv subjects

Kyohei Itakura

Publications and source records attributed to Kyohei Itakura.

3 recordsLinked to original sources

arXiv2020

Stationary scattering theory for repulsive Hamiltonians

In the present paper we discuss stationary scattering theory for repulsive Hamiltonians. We show the existence and completeness of stationary wave operators and unitarity of the scattering matrix. Moreover we completely characterize asymptotic behaviors of generalized eigenfunctions with minimal growth in terms of the scattering matrix. In our argument the radiation condition bounds for limiting resolvents play major roles. In fact, it is used to construct the stationary wave operators.

math-ph↗

arXiv2017

Limiting absorption principle and radiation condition for repulsive Hamiltonians

For spherically symmetric repulsive Hamiltonians we prove the Besov bound, the radiation condition bounds and the limiting absorption principle. The Sommerfeld uniqueness result also follows as a corollary of these. In particular, the Hamiltonians considered in this paper cover the case of inverted harmonic oscillator. In the proofs of our theorems, we mainly use a commutator argument invented recently by Ito and Skibsted. This argument is simple and elementary, and dose not employ energy cut-offs or the microlocal analysis.

math-ph↗

arXiv2017

Rellich's theorem for spherically symmetric repulsive Hamiltonians

For spherically symmetric repulsive Hamiltonians we prove Rellich's theorem, or identify the largest weighted space of Agmon-Hörmander type where the generalized eigenfunctions are absent. The proof is intensively dependent on commutator arguments. Our novelty here is a use of conjugate operator associated with some radial flow, not with dilations and translations. Our method is simple and elementary, and does not employ any advanced tools such as the operational calculus or the Fourier analysis.

math.FA↗