Title: $L^p$ Norms of Eigenfunctions on Regular Graphs and on the Sphere
Abstract: We prove upper bounds on the $L^p$ norms of eigenfunctions of the discrete Laplacian on regular graphs. We then apply these ideas to study the $L^p$ norms of joint eigenfunctions of the Laplacian and an averaging operator over a finite collection of algebraic rotations of the $2$-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.
Publication Year: 2017
Publication Date: 2017-10-30
Language: en
Type: preprint
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