We obtain new quantitative estimates on Weyl Law remainders under dynamical
assumptions on the geodesic flow. On a smooth compact Riemannian manifold (M, g) of …

We develop new techniques for studying concentration of Laplace eigenfunctions ϕ λ as
their frequency, λ, grows. The method consists of controlling ϕ λ⁢(x) by decomposing ϕ λ …

This work concerns $ L^ p $ norms of high energy Laplace eigenfunctions, $(-\Delta_g-
\lambda^ 2)\phi_\lambda= 0$, $\|\phi_\lambda\| _ {L^ 2}= 1$. In 1988, Sogge gave optimal …

Given a Riemannian manifold endowed with its Laplace-Beltrami operator, consider the
associated spectral projector on a thin interval. As an operator from L2 to Lp, what is its …

Let (M, g) be a compact Riemannian manifold of dimension n and P_1:=-h^ 2 Δ _g+ V (x)-
E_1 P 1:=-h 2 Δ g+ V (x)-E 1 so that dp_1 ≠ 0 dp 1≠ 0 on p_1= 0 p 1= 0. We assume that …

Let {ej} be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian
manifold (M, g). Let H⊂ M be a submanifold and {ψ k} be an orthonormal basis of Laplace …

Let $(M, g) $ be a smooth, compact Riemannian manifold and ${\lbrace\phi\lambda\rbrace}
$ an $ L^ 2$-normalized sequence of Laplace eigenfunctions, $-\Delta_g\phi_\lambda …

This book aims to explain the concepts behind the geodesic beam method that we have
developed to study the behavior of high energy eigenfunctions. The idea for geodesic …

Geodesic biangles and Fourier coefficients of restrictions of eigenfunctions Page 1 PURE and
APPLIED ANALYSIS msp EMMETT L. WYMAN, YAKUN XI AND STEVE ZELDITCH GEODESIC …

Burq-G\'erard-Tzvetkov and Hu established $ L^ p $ estimates for the restriction of Laplace-
Beltrami eigenfunctions to submanifolds. We investigate the eigenfunctions of the Schr\" …