On the dimension of divergence sets of dispersive equations

JA Barceló; Jonathan Bennett; A Carbery; KM Rogers

doi:10.1007/s00208-010-0529-z

On the dimension of divergence sets of dispersive equations

JA Barceló, Jonathan Bennett, A Carbery, KM Rogers

Mathematics

Research output: Contribution to journal › Article

21 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	599-622
Number of pages	24
Journal	Mathematische Annalen
Volume	349
Issue number	3
DOIs	https://doi.org/10.1007/s00208-010-0529-z
Publication status	Published - 1 Mar 2011

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10.1007/s00208-010-0529-z

New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics
Bennett, J. (Principal Investigator)
Engineering & Physical Science Research Council
3/01/07 → 2/01/10
Project: Research Councils

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abstract = "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.",

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AU - Carbery, A

AU - Rogers, KM

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N2 - 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.

AB - 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.

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DO - 10.1007/s00208-010-0529-z

M3 - Article

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VL - 349

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JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3

ER -

On the dimension of divergence sets of dispersive equations

Abstract

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New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics

Cite this