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(2018). Lp Norms of Eigenfunctions on Regular Graphs and on the Sphere. International Mathematics Research

. 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.