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\(L^p\) Norms and Support of Eigenfunctions on Graphs

  • Etienne Le MassonEmail author
  • Mostafa Sabri
Article
  • 11 Downloads

Abstract

This article is concerned with properties of delocalization for eigenfunctions of Schrödinger operators on large finite graphs. More specifically, we show that the eigenfunctions have a large support and we assess their \(\ell ^p\)-norms. Our estimates hold for any fixed, possibly irregular graph, in prescribed energy regions, and also for certain sequences of graphs such as N-lifts.

Notes

Acknowledgements

E.L.M. was supported by the Marie Skłodowska-Curie Individual Fellowship grant 703162. M.S. was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Université de Cergy-PontoiseCergy-Pontoise CedexFrance
  2. 2.Department of Mathematics, Faculty of ScienceCairo UniversityCairoEgypt
  3. 3.Laboratoire de Mathématique, UMR 8628 du CNRSUniversité Paris Sud XIOrsay CedexFrance

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