Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues
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]
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|Source:||Duke Mathematical Journal|
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