# Growth rates of Laplace eigenfunctions on the unit disk

Research paper by Guillaume Lavoie, Guillaume Poliquin

Indexed on: 31 Mar '20Published on: 27 Mar '20Published in: arXiv - Mathematics - Spectral Theory

#### Abstract

We give a description of the growth rates of $L^2$-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.