Abstract
Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between the M-function as an analytic function of a spectral parameter and the spectrum of the extension. We also give an example where the M-function does not contain the whole spectral information of the resolvent, and show that the results can be applied to elliptic PDEs where the M-function corresponds to the Dirichlet to Neumann map.
Original language | English |
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Pages (from-to) | 700-718 |
Number of pages | 19 |
Journal | Journal of the London Mathematical Society |
Volume | 77 |
Issue number | 3 |
DOIs | |
Publication status | Published - Mar 2008 |