Bounds for spectral projectors on tori

Abstract

We investigate norms of spectral projectors on thin spherical shells for the Laplacian on tori. This is closely related to the boundedness of resolvents of the Laplacian, and to the boundedness of $L^p$ norms of eigenfunctions of the Laplacian. We formulate a conjecture, and partially prove it.

18 pages, statement of Theorem 1.2 simplified with resulting changes in Corollary 1.3

Cited by in corpus (2)

• Bounds for spectral projectors on the Euclidean cylinder
• Sharp Spectral Projection Estimates for the Torus at $p_c=\frac{2(n+1)}{n-1}$