Refined asymptotics for eigenvalues on domains of infinite measure

Details Refined asymptotics for eigenvalues on domains of infinite measure Refined asymptotics for eigenvalues on domains of infinite measure

2009-06-12

arxiv.org/abs/0906.2198v1

Mathematics

Analysis of PDEs

18 pages, 2 figures

Scientific paper

In this work we study the asymptotic distribution of eigenvalues in
one-dimensional open sets. The method of proof is rather elementary, based on
the Dirichlet lattice points problem, which enable us to consider sets with
infinite measure. Also, we derive some estimates for the the spectral counting
function of the Laplace operator on unbounded two-dimensional domains.

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