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Eigenfunction
scarring and improvements in $L^\infty$ bounds
Jeffrey Galkowski and John A. Toth |
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Vol. 11 (2018), No. 3, 801–812
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Abstract |
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We study the relationship between growth of eigenfunctions and their concentration as measured by defect measures. In particular, we show that scarring in the sense of concentration of defect measure on certain submanifolds is incompatible with maximal growth. In addition, we show that a defect measure which is too diffuse, such as the Liouville measure, is also incompatible with maximal eigenfunction growth. |
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Keywords
eigenfunction, sup norms, defect measure
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Mathematical Subject Classification 2010
Primary: 35P20, 58J50
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Milestones
Received: 4 April 2017
Revised: 18 August 2017
Accepted: 16 October 2017
Published: 22 November 2017
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Authors |
| Jeffrey Galkowski | |
| Department of Mathematics and
Statistics McGill University Montréal, QC Canada |
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| John A. Toth | |
| Department of Mathematics and
Statistics McGill University Montréal, QC Canada |
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