{"paper":{"title":"Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Ian Wood, Malcolm Brown, Marco Marletta, Serguei Naboko","submitted_at":"2007-04-19T15:33:09Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2562","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}