2025/01/31 by Ambre Chabert, Chabert, Ambre · 1 citation
Materials Science · Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Quasicrystal Structures and Properties #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2502.00143
openalex publication_date 2025/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a compact surface of revolution with Laplace-beltrami operator Δ, we consider the spectral projector Pλ,δ on a polynomially narrow frequency interval [λ-δ,λ+ δ], which is associated to the self-adjoint operator √(-Δ). For a large class of surfaces of revolution, and after excluding small disks around the poles, we prove that the L2 → L∞ norm of Pλ,δ is of order λ(1)/(2) δ(1)/(2) up to δ≥ λ-(1)/(32). We adapt the microlocal approach introduced by Sogge for the case δ= 1, by using the Quantum Completely Integrable structure of surfaces of revolution introduced by Colin de Verdière. This reduces the analysis to a number of estimates of explicit oscillatory integrals, for which we introduce new quantitative tools.This is the first sharp result in the case δ≪ 1 beyond the case of locally symmetric surfaces (torus, sphere, arithmetic hyperbolic surfaces).