Lp norms of eigenfunctions on regular graphs and on the sphere

Shimon Brooks, Etienne Le Masson

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Abstract

We prove upper bounds on the Lp norms of eigenfunctions of the discrete Laplacian on regular graphs. We then apply these ideas to study the Lp norms of joint eigenfunctions of the Laplacian and an averaging operator over a finite collection of algebraic rotations of the two-sphere. Under mild conditions, such joint eigenfunctions are shown to satisfy for large p the same bounds as those known for Laplace eigenfunctions on a surface of non-positive curvature.

Original languageEnglish
Pages (from-to)3201-3228
Number of pages28
JournalInternational Mathematics Research Notices
Volume2020
Issue number11
DOIs
StatePublished - 2021

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© The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions

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