5 papers
Inverse scattering for -body time-decaying harmonic oscillators
Atsuhide Ishida
In the previous study (Ishida, 2025), the author proved the uniqueness of short-range potential functions using the Enss-Weder time-dependent method (Enss and Weder, 1995) for a tw…
Special potentials for relativistic Laplacians I: Fractional Rollnik-class
Giacomo Ascione, Atsuhide Ishida, József LÅrinczi
We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz pote…
Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type
Atsuhide Ishida
We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonians of quadratic type. The time-dependent coefficient on the repulsive term decay…
On Schrödinger equation with square and inverse-square potentials
Atsuhide Ishida, Masaki Kawamoto
In this paper, we study the linear and nonlinear Schrödinger equations with a time-decaying harmonic oscillator and inverse-square potential. This model retains a form of scale in…
Minimal velocity bound for Schroedinger-type operator with fractional powers
Atsuhide Ishida
It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the m…