Let $ g $ be a Hecke-Maass cusp form on the modular surface $\mathrm {SL} _2 (\mathbb
{Z})\backslash\mathbb {H} $, namely an $ L^ 2$-normalised nonconstant Laplacian …

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 …

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 smooth, compact Riemannian manifold and ${\lbrace\phi\lambda\rbrace}
$ an $ L^ 2$-normalized sequence of Laplace eigenfunctions, $-\Delta_g\phi_\lambda …

In this paper, we prove $ L^ 2\to L^ p $ estimates, where $ p> 2$, for spectral projectors on a
wide class of hyperbolic surfaces. More precisely, we consider projections in small spectral …

It is well known that uniform resolvent estimates imply spectral cluster estimates. We show
that the converse is also true in some cases. In particular, Sogge's universal spectral cluster …

Consider a 2-dimensional smooth Riemannian manifold $ M $, and let $ P (h) $ be a
semiclassical pseudodifferential operator on $ M $. Assume that $ f= f (h) $ is an $ O (h) …

In this paper, we prove L2→ Lp estimates, where p> 2, for spectral projectors on a wide
class of hyperbolic surfaces. More precisely, we consider projections in small spectral …

On the canonical 2-sphere and for Schrödinger eigenfunctions, we obtain a simple
geometric criterion on the potential under which we can improve, near a given point and for …