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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Number of pages | 28 |
Journal | International Mathematics Research Notices |
Early online date | 28 May 2018 |
DOIs | |
Publication status | E-pub ahead of print - 28 May 2018 |