Abstract
We consider L1→L∞ estimates for the time evolution of Hamiltonians H=−Δ+V in dimensions d=1 and d=3 with bound We require decay of the potentials but no regularity. In d=1 the decay assumption is ∫(1+|x|)|V(x)|dx<∞, whereas in d=3 it is |V(x)|≤C(1+|x|)−3−.
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Communicated by B. Simon
Supported by the NSF grant DMS-0070538 and a Sloan fellowship.
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Goldberg, M., Schlag, W. Dispersive Estimates for Schrödinger Operators in Dimensions One and Three. Commun. Math. Phys. 251, 157–178 (2004). https://doi.org/10.1007/s00220-004-1140-5
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DOI: https://doi.org/10.1007/s00220-004-1140-5