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- W2157777458 abstract "This is a continuation of the paper (3). We consider the Dirichlet Laplacian in a family of unbounded domains {x ∈ R, 0 <y<� h(x)} .T he main assumption is that x = 0 is the only point of global maximum of the pos- itive, continuous function h(x). We show that the number of eigenvalues lying below the essential spectrum indefinitely grows as � → 0, and find the two-term asymptotics in � → 0 of each eigenvalue and the one-term asymptotics of the corresponding eigenfunction. The asymptotic formulae obtained involve the eigenvalues and eigenfunctions of an auxiliary ODE on R that depends only on the behavior of h(x )a sx → 0. The proof is based on a detailed study of the resolvent of the operator ∆." @default.
- W2157777458 created "2016-06-24" @default.
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- W2157777458 date "2008-12-17" @default.
- W2157777458 modified "2023-09-23" @default.
- W2157777458 title "On the spectrum of the Dirichlet Laplacian in a narrow infinite strip" @default.
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- W2157777458 doi "https://doi.org/10.1090/trans2/225/07" @default.
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