Abstract

The three-dimensional Schrödinger propogator eitH, H = -Δ + V, is a bounded map from L1 to L with norm controlled by |t|-3/2 provided the potential satisfies two conditions: An integrability condition limiting the singularities and decay of V, and a zero-energy spectral condition on H. This is shown by expressing the spectral measure of H in terms of its resolvents and proving a family of Lp mapping estimates for the resolvents. Previous results in this direction had required V to satisfy explicit pointwise bounds.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 731-750
Launched on MUSE
2006-05-24
Open Access
No
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