Bounds for spectral projectors on generic tori

Pierre Germain; Simon L Rydin Myerson

doi:10.1007/s00208-022-02547-w

Bounds for spectral projectors on generic tori

Math Ann. 2024;388(1):731-767. doi: 10.1007/s00208-022-02547-w. Epub 2022 Dec 23.

Authors

Pierre Germain¹, Simon L Rydin Myerson²

Affiliations

¹ Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185 USA.
² Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL United Kingdom.

Abstract

We investigate norms of spectral projectors on thin spherical shells for the Laplacian on generic tori, including generic rectangular tori. We state a conjecture and partially prove it, improving on previous results concerning arbitrary tori.

Keywords: 11D75; 11H06; 11L07; 11P21; 42A45; 42B15.