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2018 Eigenfunction scarring and improvements in $L^\infty$ bounds
Jeffrey Galkowski, John A. Toth
Anal. PDE 11(3): 801-812 (2018). DOI: 10.2140/apde.2018.11.801

Abstract

We study the relationship between L growth of eigenfunctions and their L2 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.

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Jeffrey Galkowski. John A. Toth. "Eigenfunction scarring and improvements in $L^\infty$ bounds." Anal. PDE 11 (3) 801 - 812, 2018. https://doi.org/10.2140/apde.2018.11.801

Information

Received: 4 April 2017; Revised: 18 August 2017; Accepted: 16 October 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 06820940
MathSciNet: MR3738263
Digital Object Identifier: 10.2140/apde.2018.11.801

Subjects:
Primary: 35P20, 58J50

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 3 • 2018
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