Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

B. Malcolm Brown, Ian Wood, Marco Marletta, Serguei Naboko

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)
164 Downloads (Pure)

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 languageEnglish
Pages (from-to)700-718
Number of pages19
JournalJournal of the London Mathematical Society
Volume77
Issue number3
DOIs
Publication statusPublished - Mar 2008

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