M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems

Details M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems

2008-03-26

arxiv.org/abs/0803.3630v3

Mathematics

Spectral Theory

33 pages, explanations expanded, accepted for publication in Mathematische Nachrichten

Scientific paper

In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the operator to possess spectral points that can not be detected by the M-function.

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