Bounds for spectral projectors on tori

Published 27 Apr 2021 in math.AP, math.CA, and math.NT | (2104.13274v4)

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.

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