Israel Journal of Mathematics

, Volume 77, Issue 1, pp 1–16

A remark on Schrödinger operators


  • J. Bourgain
    • Département de MathématiqueIHES

DOI: 10.1007/BF02808007

Cite this article as:
Bourgain, J. Israel J. Math. (1992) 77: 1. doi:10.1007/BF02808007


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=tu. The main result is thatu(x, t) →f(x) almost everywhere fort → 0 iffHp(R2), wherep may be chosen <1/2. To get this result (improving on Vega’s work, see [6]), we devise a strategy to capture certain cancellations, which we believe has other applications in related problems.

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© Hebrew University 1992