Bounds for spectral projectors on generic tori
Pierre Germain, Simon L. Rydin Myerson
TL;DR
This paper studies the behavior of spectral projectors on thin spherical shells for the Laplacian on generic tori, proposing a conjecture and providing partial proofs to improve existing bounds.
Contribution
It introduces a new conjecture and offers partial proofs that enhance previous bounds for spectral projectors on generic tori.
Findings
Improved bounds for spectral projectors on generic tori
Partial proof supporting the conjecture
Enhanced understanding of spectral behavior on tori
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.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Spectral Theory in Mathematical Physics · Mathematical Dynamics and Fractals