On the dimension of divergence sets of dispersive equations

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We refine results of Carleson, Sjogren and Sjolin regarding the pointwise convergence to the initial data of solutions to the Schrodinger equation. We bound the Hausdorff dimension of the sets on which convergence fails. For example, with initial data in, the sets of divergence have dimension at most one.


Original languageEnglish
Pages (from-to)599-622
Number of pages24
JournalMathematische Annalen
Issue number3
Publication statusPublished - 1 Mar 2011