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 language | English |
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Pages (from-to) | 3201-3228 |
Number of pages | 28 |
Journal | International Mathematics Research Notices |
Volume | 2020 |
Issue number | 11 |
DOIs | |
State | Published - 2021 |
Bibliographical note
Publisher Copyright:© The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions
Funding
This work was supported by the Israel Science Foundation [1119/13 to S.B.] and by the Marie This work was supported by the Israel Science Foundation [1119/13 to S.B.] and by the Marie Sk?odowska-Curie Individual Fellowship [703162 to E.L.M.].
Funders | Funder number |
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Marie | |
Horizon 2020 Framework Programme | 703162 |
Israel Science Foundation | 1119/13 |