{"paper":{"title":"On eigenvalues of self-adjoint extensions for defect larger than one","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Annemarie Luger, Jakob Reiffenstein","submitted_at":"2026-06-03T08:48:35Z","abstract_excerpt":"Self-adjoint extensions of a symmetric operator are parametrised by Krein's formula, in which the $Q$-function interacts with another analytic function (the parameter). We obtain a characterisation of the eigenvalues, isolated or not, of a given self-adjoint extension in terms of these two functions. The setting is highly general, covering symmetric operators with arbitrary defect in a Hilbert or Pontryagin space. Of independent interest is our newly developed tool, the \\emph{generalised value} of a generalised Nevanlinna function, for which we give both a function-theoretic and an operator-th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04611","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04611/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}