On the dimension of divergence sets of dispersive equations

We refine results of Carleson, Sjögren and Sjölin regarding the pointwise convergence to the initial data of solutions to the Schrödinger 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 mo...

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Bibliographic Details
Published inMathematische annalen Vol. 349; no. 3; pp. 599 - 622
Main Authors Barceló, Juan Antonio, Bennett, Jonathan, Carbery, Anthony, Rogers, Keith M.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.03.2011
Subjects
Mathematics
Mathematics and Statistics
Hausdorff Dimension
Pointwise Convergence
Fourier Extension
Bessel Potential
Fourier Inversion Formula
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Summary:We refine results of Carleson, Sjögren and Sjölin regarding the pointwise convergence to the initial data of solutions to the Schrödinger 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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-010-0529-z