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Compactness and Eigenfunctions

1993
In previous chapters we explored the connection between compactness for composition operators and the existence of angular derivatives for their inducing maps. Here we begin to study how compactness affects the eigen-functions of a composition operator.
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Approach to energy eigenvalues and eigenfunctions from nonperturbative regions of eigenfunctions

Physical Review E, 2001
We study the approach to energy eigenvalues and eigenfunctions of Hamiltonian matrices with band structure from diagonalization of their truncated matrices. Making use of a generalization of Brillouin-Wigner perturbation theory, it is shown that in order to obtain approximate energy eigenvalues and eigenfunctions the sizes of truncated matrices should ...
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