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Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues

Barnett, Alex; Hassell, Andrew; Tacy, Melissa


For smooth bounded domains in Rn, we prove upper and lower L2 bounds on the boundary data of Neumann eigenfunctions, and we prove quasiorthogonality of this boundary data in a spectral window. The bounds are tight in the sense that both are independent of the eigenvalues; this is achieved by working with an appropriate norm for boundary functions, which includes a spectral weight, that is, a function of the boundary Laplacian. This spectral weight is chosen to cancel concentration at the...[Show more]

CollectionsANU Research Publications
Date published: 2018-11-01
Type: Journal article
Source: Duke Mathematical Journal
DOI: 10.1215/00127094-2018-0031


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