Galkowski, J;
Toth, JA;
(2017)
Eigenfunction scarring and improvements in L∞ Bounds.
Analysis & PDE
, 11
(3)
pp. 801-812.
10.2140/apde.2018.11.801.
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Abstract
We study the relationship between L∞ growth of eigenfunctions and their L^{2} 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 L∞ 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.
| Type: | Article |
|---|---|
| Title: | Eigenfunction scarring and improvements in L∞ Bounds |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/apde.2018.11.801 |
| Publisher version: | https://doi.org/10.2140/apde.2018.11.801 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | eigenfunction, sup norms, defect measure |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10083903 |
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