In this talk I will discuss recent and upcoming results on the boundedness of spectral projectors. The seminal work of C. Sogge gives the optimal result on any Riemannian manifold with bounded geometry for spectral windows of size 1. However when the width is smaller, the spectral projector bounds become sensitive to the global geometry of the underlying manifold. I will focus on the case of hyperbolic surfaces of infinite area, and present new estimates that hold universally in that setting. This is joint work with Jean-Philippe Anker and Pierre Germain.
Spectral projector bounds on hyperbolic surfaces of infinite area Sponsored by the Meyer Fund
Spectral projector bounds on hyperbolic surfaces of infinite area