DISPERSIVE ESTIMATES FOR SCHRODINGER OPERATORS IN DIMENSION TWO WITH OBSTRUCTIONS AT ZERO ENERGY

作者：Erdogan M Burak; Green William R^*

来源：Transactions of the American Mathematical Society, 2013, 365(12): 6403-6440.

We investigate L-1(R-2) -> L-infinity(R-2) dispersive estimates for the Schrodinger operator H = -Delta + V when there are obstructions, resonances or an eigenvalue, at zero energy. In particular, we show that the existence of an s-wave resonance at zero energy does not destroy the t(-1) decay rate. We also show that if there is a p-wave resonance or an eigenvalue at zero energy, then there is a time dependent operator F-t satisfying parallel to F-t parallel to(L1 -> L infinity) less than or similar to 1 such that
parallel to e(itH) P-ac - F-t parallel to(L1 -> L infinity) less than or similar to vertical bar t vertical bar(-1), for vertical bar t vertical bar > 1.
We also establish a weighted dispersive estimate with t(-1) decay rate in the case when there is an eigenvalue at zero energy but no resonances.

• 出版日期2013-12