caa a22 4500 469068868 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19920201xx s 000 0 eng 10.1007/BF02808007 doi (NATIONALLICENCE)springer-10.1007/BF02808007 Bourgain J. Département de Mathématique, IHES, 35 route de Chartres, Bures-sur-Yvette, France aut A remark on Schrödinger operators [Elektronische Daten] [J. Bourgain] 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 [6]), we devise a strategy to capture certain cancellations, which we believe has other applications in related problems. Hebrew University, 1992 Israel Journal of Mathematics Springer-Verlag 77/1-2(1992-02-01), 1-16 0021-2172 77:1-2<1 1992 77 11856 https://doi.org/10.1007/BF02808007 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808007 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bourgain J. Département de Mathématique, IHES, 35 route de Chartres, Bures-sur-Yvette, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 77/1-2(1992-02-01), 1-16 0021-2172 77:1-2<1 1992 77 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer