72 citations · 139 across the 21 of their papers we have counts for
23 papers
Nonconcentration of eigenfunctions in Microlocal Kakeya-Nikodym norms: a phase space approach
Matthew D. Blair
Previous works of the author and Sogge [BS17], [BS18] showed the significance of microlocal Kakeya-Nikodym averages in improving bounds on (approximate) eigenfunctions of the…
Strichartz estimates for the Schrödinger equation on negatively curved compact manifolds
Matthew D. Blair, Xiaoqi Huang, Christopher D. Sogge
We obtain improved Strichartz estimates for solutions of the Schrödinger equation on negatively curved compact manifolds which improve the classical universal results results of Bu…
Improved spectral projection estimates
Matthew D. Blair, Xiaoqi Huang, Christopher D. Sogge
We obtain new improved spectral projection estimates on manifolds of non-positive curvature, including sharp ones for relatively large spectral windows for general tori. Our result…
The Van Vleck Formula on Ehrenfest time scales and stationary phase asymptotics for frequency-dependent phases
Matthew D. Blair
The Van Vleck formula is a semiclassical approximation to the integral kernel of the propagator associated to a time-dependent Schrödinger equation. Under suitable hypotheses, we p…
Uniform Sobolev Estimates on compact manifolds involving singular potentials
Matthew D. Blair, Xiaoqi Huang, Yannick Sire +1
We obtain generalizations of the uniform Sobolev inequalities of Kenig, Ruiz and the fourth author \cite{KRS} for Euclidean spaces and Dos Santos Ferreira, Kenig and Salo \cite{DKS…
Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials
Matthew D. Blair, Yannick Sire, Christopher D. Sogge
We obtain quasimode, eigenfunction and spectral projection bounds for Schrödinger operators, , on compact Riemannian manifolds of dimension , which ex…