A remark on Schrödinger operators
- J. Bourgain
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We study the almost everythere convergence to the initial dataf(x)=u(x, 0) of the solutionu(x, t) of the two-dimensional linear Schrödinger equation Δu=iϖ t u. The main result is thatu(x, t) →f(x) almost everywhere fort → 0 iff ∈H p (R2), wherep may be chosen <1/2. To get this result (improving on Vega’s work, see ), we devise a strategy to capture certain cancellations, which we believe has other applications in related problems.
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- A remark on Schrödinger operators
Israel Journal of Mathematics
Volume 77, Issue 1-2 , pp 1-16
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- J. Bourgain (1)
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- 1. Département de Mathématique, IHES, 35 route de Chartres, Bures-sur-Yvette, France