Comptes Rendus
Harmonic analysis
Bounds for spectral projectors on the Euclidean cylinder
Pierre Germain1  ; Simon Myerson2 
1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, N.Y. 10012-1185, USA
2 Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL, United Kingdom
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1257-1262

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.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.378

Pierre Germain 1; Simon Myerson 2

1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, N.Y. 10012-1185, USA
2 Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL, United Kingdom
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Bounds for spectral projectors on the {Euclidean} cylinder},
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Pierre Germain; Simon Myerson. Bounds for spectral projectors on the Euclidean cylinder. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1257-1262. doi: 10.5802/crmath.378

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