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Growth rates of Laplace eigenfunctions on the unit disk

Spectral Theory 2020-03-31 v1

Abstract

We give a description of the growth rates of L2L^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.

Keywords

Cite

@article{arxiv.2003.12592,
  title  = {Growth rates of Laplace eigenfunctions on the unit disk},
  author = {Guillaume Lavoie and Guillaume Poliquin},
  journal= {arXiv preprint arXiv:2003.12592},
  year   = {2020}
}

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19 pages