Provides counterexamples proving that 1D wave operators W±(H,−Δ) are unbounded on L¹(ℝ) and L∞(ℝ) for bounded compactly supported non-zero V in generic cases and exceptional cases where lim x→−∞ f+(0,x)≠1, and unbounded from L∞ to BMO in the latter.
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Counterexamples to the $L^1$ and $L^{\infty}$ boundedness of the one-dimensional wave operators
Provides counterexamples proving that 1D wave operators W±(H,−Δ) are unbounded on L¹(ℝ) and L∞(ℝ) for bounded compactly supported non-zero V in generic cases and exceptional cases where lim x→−∞ f+(0,x)≠1, and unbounded from L∞ to BMO in the latter.