A spectral condition for the control of eigenfunctions of Baouendi-Grushin type operators

2023/12/07 by Mohammad Harakeh, Harakeh, Mohammad, Luc Hillairet +1
Computer Science · Mathematics · #35P15 58J50 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2312.04359

openalex publication_date 2023/12/07 · openalex created_date 2023/12/09 · openalex updated_date 2026/07/28

Abstract

We study a concentration inequality for eigenfunctions of a Baouendi-Grushin operator on a cylinder or a torus. Using separation of variables, we prove that this inequality holds under a spectral multiplicity condition. Using Albert-Uhlenbeck's theory, we then prove that this spectral condition is generically true for such sub-elliptic operators.

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