An improved spectral inequality for sums of eigenfunctions

2023/12/27 by Axel Osses, Osses, Axel, Faouzi Triki +1 · 1 citation
Computer Science · Mathematics · #35P05 #93C20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Approximation and Integration #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2312.16495

openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a new spectral inequality for the quantified estimation of the H^s-norm, s≥ 0 of a finite linear combination of eigenfunctions in a domain in terms of its H^s-norm in a strictly open subset of the whole domain. The corresponding upper bound depends exponentially on the square root of the frequency number associated to the linear combination.

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