Harmonic analysis
Bounds for spectral projectors on the Euclidean cylinder
Comptes Rendus. Mathématique, Volume 360 (2022) no. G11, pp. 1257-1262.

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

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DOI: 10.5802/crmath.378
Germain, Pierre 1; Myerson, Simon 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
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Germain, Pierre; Myerson, Simon. Bounds for spectral projectors on the Euclidean cylinder. Comptes Rendus. Mathématique, Volume 360 (2022) no. G11, pp. 1257-1262. doi : 10.5802/crmath.378. http://www.numdam.org/articles/10.5802/crmath.378/

[1] Barron, Alexander; Christ, Michael; Pausader, Benoît Global endpoint strichartz estimates for Schrödinger equations on the cylinder ×𝕋, Nonlinear Anal., Theory Methods Appl., Volume 206 (2021), 112172 | Zbl

[2] Bourgain, Jean Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation, Geom. Funct. Anal., Volume 3 (1993) no. 3, pp. 209-262 | DOI | MR | Zbl

[3] Bourgain, Jean; Demeter, Ciprian The proof of the l 2 decoupling conjecture, Ann. Math., Volume 182 (2015) no. 1, pp. 351-389 | DOI | MR | Zbl

[4] Germain, Pierre; Myerson, Simon L. R. Bounds for spectral projectors on tori (2021) (https://arxiv.org/abs/2104.13274v1)

[5] Sogge, Christopher D. Fourier integrals in classical analysis, Cambridge Tracts in Mathematic, 105, Cambridge University Press, 1993 | DOI | Zbl

[6] Takaoka, Hideo; Tzvetkov, Nikolay On 2D nonlinear schrödinger equations with data on ×𝕋, J. Funct. Anal., Volume 182 (2001) no. 2, pp. 427-442 | DOI | Zbl

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