43 citations · 74 across the 21 of their papers we have counts for
8 papers · 1 filter
Eigenvalue spacing for 1D singular Schrödinger operators
Luc Hillairet, Jeremy L. Marzuola
The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schrödinger operators with singular potentials on the half-line.…
Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results
Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat
We establish small-time asymptotic expansions for heat kernels of hypoelliptic Hörmander operators in a neighborhood of the diagonal, generalizing former results obtained in partic…
On resonances generated by conic diffraction
Luc Hillairet, Jared Wunsch
We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenl…
Spectral stability under removal of small capacity sets and applications to Aharonov-Bohm operators
Laura Abatangelo, Veronica Felli, Luc Hillairet +1
We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenva…
Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction
G. Austin Ford, Andrew Hassell, Luc Hillairet
We investigate the singularities of the trace of the half-wave group, , on Euclidean surfaces with conical singularities . We compute the leadi…
Nonconcentration in partially rectangular billiards
Luc Hillairet, Jeremy L. Marzuola
In specific types of partially rectangular billiards we estimate the mass of an eigenfunction of energy in the region outside the rectangular set in the high-energy limit. We u…