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Examines boundedness of wave operators in fourth order Schrödinger operators, implying potential for greater understanding in scattering theory.
We prove that wave operators of scattering theory for fourth order Schrödinger operators [Formula: see text] on [Formula: see text] with real potentials [Formula: see text] such that [Formula: see text] and [Formula: see text] for an [Formula: see text], [Formula: see text], are bounded in [Formula: see text] for all [Formula: see text] if [Formula: see text] is regular at zero in the sense that there are no non-trivial solutions to [Formula: see text] such that [Formula: see text] and if positive eigenvalues are absent from [Formula: see text]. This reduces [Formula: see text]-mapping properties of functions [Formula: see text] of [Formula: see text] to those of Fourier multipliers [Formula: see text].
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Galtbayar et al. (2026) studied this question.
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