Browsing by Author "Yajima, Kenji"
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Item Lp-boundedness of wave operators for the three-dimensional multi-centre point interaction(2017-04-13) Dell'Antonio, Gianfausto; Michelangeli, Alessandro; Scandone, Raffaele; Yajima, Kenji; MathematicsWe prove that, for arbitrary centres and strengths, the wave operators for three dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3) for 1 < p < 3 and unbounded otherwise.Item On wave operators for Schrödinger operators with threshold singuralities in three dimensions(SISSA, 2016-06) Yajima, Kenji; MathematicsWe show that wave operators for three dimensional Schr\"odinger operators H=−Δ+V with threshold singularities are bounded in L1(R3) if and only if zero energy resonances are absent from H and the existence of zero energy eigenfunctions does not destroy the L1-boundedness of wave operators for H with the regular threshold behavior. We also show in this case that they are bounded in Lp(R3) for all 1≤p≤∞ if all zero energy eigenfunctions ϕ(x) have vanishing first three moments: ∫R3xαV(x)ϕ(x)dx=0, |α|=0,1,2.Item Two-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operators(SISSA, 2019-10-10) Cornean, Horia D.; Michelangeli, Alessandro; Yajima, Kenji