Bounds for spectral projectors on the Euclidean cylinder

TL;DR

This paper establishes near-optimal bounds for spectral projectors on the Euclidean cylinder, leveraging the unbounded dimension to provide a concise proof, advancing understanding of spectral behavior in this setting.

Contribution

It introduces essentially optimal bounds for spectral projectors on the Euclidean cylinder, utilizing the unbounded dimension for a simplified, self-contained proof.

Findings

Derived near-optimal bounds for spectral projectors on the Euclidean cylinder.

Demonstrated the advantage of the unbounded dimension in simplifying proofs.

Provided a compact, self-contained proof contrasting previous approaches.

Abstract

We prove essentially optimal bounds for norms of spectral projectors on thin spherical shells for the Laplacian on the cylinder (R/Z)*R. In contrast to previous investigations into spectral projectors on tori, having one unbounded dimension available permits a compact self-contained proof.