On the dimension of divergence sets of dispersive equations

Juan Antonio Barcelo; Jonathan Bennett; Anthony Carbery; Keith M. Rogers

doi:10.1007/s00208-010-0529-z

On the dimension of divergence sets of dispersive equations

Juan Antonio Barcelo, Jonathan Bennett, Anthony Carbery, Keith M. Rogers

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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 - Mar 2011

Keywords / Materials (for Non-textual outputs)

SCHRODINGER-EQUATION
FOURIER-TRANSFORMS
POINTWISE CONVERGENCE
SPHERICAL AVERAGES
BILINEAR APPROACH
MAXIMAL OPERATOR
INEQUALITIES
RESTRICTION
MULTIPLIERS

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10.1007/s00208-010-0529-z

On the dimension of divergence sets of dispersive equationsSubmitted manuscript, 653 KB

http://link.springer.com/article/10.1007%2Fs00208-010-0529-z

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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 - Antonio Barcelo, Juan

AU - Bennett, Jonathan

AU - Carbery, Anthony

AU - Rogers, Keith M.

PY - 2011/3

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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.

KW - SCHRODINGER-EQUATION

KW - FOURIER-TRANSFORMS

KW - POINTWISE CONVERGENCE

KW - SPHERICAL AVERAGES

KW - BILINEAR APPROACH

KW - MAXIMAL OPERATOR

KW - INEQUALITIES

KW - RESTRICTION

KW - MULTIPLIERS

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U2 - 10.1007/s00208-010-0529-z

DO - 10.1007/s00208-010-0529-z

M3 - Article

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VL - 349

SP - 599

EP - 622

JO - Mathematische annalen

JF - Mathematische annalen

IS - 3

ER -

On the dimension of divergence sets of dispersive equations

Abstract

Keywords / Materials (for Non-textual outputs)

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