Lp Norms of Eigenfunctions on Regular Graphs and on the Sphere

Shimon Brooks, Etienne Le Masson

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We prove upper bounds on the Lnorms 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
Number of pages28
JournalInternational Mathematics Research Notices
Early online date28 May 2018
DOIs
Publication statusE-pub ahead of print - 28 May 2018

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