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math.AP2026
On wave operators for Hardy operators with and without perturbations
Atsuhide Ishida, Konstantin Merz
We prove asymptotic completeness of the wave operators in time-dependent scattering theory which intertwine the ordinary or fractional Laplacian and the corresponding Hardy operato…
math.AP2025
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…
math.AP2024★ 2 cited
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 inv…