Communications in Mathematical Physics

, Volume 257, Issue 1, pp 87-117

First online:

Dispersive Estimates for Schrödinger Operators in Dimension Two

  • W. SchlagAffiliated withDivision of Astronomy, Mathematics, and Physics,   Email author 

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We prove L 1(ℝ2)→L (ℝ2) for the two-dimensional Schrödinger operator −Δ+V with the decay rate t −1. We assume that zero energy is neither an eigenvalue nor a resonance. This condition is formulated as in the recent paper by Jensen and Nenciu on threshold expansions for the two-dimensional resolvent.