Park City Lectures on Eigenfunctions, Lecture 5: Lp norms of ...

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Oscillation of a spherical harmonic Y l m of low degree
Oscillation of a spherical harmonic Y l m of high degree
Page 1 and 2: Park City<
Page 3 and 4: L p norms We recall that ∆ϕ λ =
Page 5 and 6: Sogge upper bounds on L p norms of
Page 7 and 8: Extremals The upper bounds are shar
Page 9: Spherical harmonics of degree k Let
Page 13 and 14: Coherent state Φ x k at x For each
Page 15 and 16: Normalized zonal harmonics On S n ,
Page 17 and 18: Gaussian Beam: maximizes L p norms
Page 19 and 20: Intuitive principle The fact that t
Page 21 and 22: Lagrangian distributions The Lagran
Page 23 and 24: What is the Lagrangian submanifold?
Page 25 and 26: Intensity plot of an ergodic eigenf
Page 27 and 28: First condition for maximal eigenfu
Page 29 and 30: Special points and submanifolds ◮
Page 31 and 32: Additional necessary conditions For
Page 33 and 34: Pole of a surface of revolution and
Page 35 and 36: Sketch of proof ◮ Suffices to sho
Page 37 and 38: Local Weyl law and L ∞ estimates
Page 39 and 40: Notation for smoothed remainder Let
Page 41 and 42: Many charts, many oscillatory integ
Page 43 and 44: Pointwise Weyl asymptotics: Safarov
Page 45 and 46: Decomposition of R 1 into loops and
Page 47 and 48: Ergodic theory at the self-focal po
Page 49 and 50: Uniform o(λ n−1 ) outside of sma
Page 51: Summing up ◮ No eigenfunction ϕ

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