Growth rates of Laplace eigenfunctions on the unit disk

2020/03/27 by Guillaume Lavoie, Lavoie, Guillaume, Guillaume Poliquin +1
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.2003.12592

19 pages

arxiv created 2020/03/27 · openalex publication_date 2020/03/27 · arxiv updated 2020/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a description of the growth rates of L²-normalized Laplace eigenfunctions on the unit disk with Dirichlet and Neumann boundary conditions. In particular, we show that the growth rates of both Dirichlet and Neumann eigenfunctions are bounded away from zero. Our approach starts with P. Sarnak growth exponents and uses several key asymptotic formulas for Bessel functions or their zeros.

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