{"paper":{"title":"Phillips symmetric operators and their extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"L. Nizhnik, S. Kuzhel","submitted_at":"2018-01-12T21:33:39Z","abstract_excerpt":"Let $S$ be a symmetric operator with equal defect numbers and let $\\mathfrak{U}$ be a set of unitary operators in a Hilbert space $\\mathfrak{H}$. The operator $S$ is called $\\mathfrak{U}$-invariant if $US=SU$ for all $U\\in\\mathfrak{U}$. Phillips \\cite{PH} constructed an example of $\\mathfrak{U}$-invariant symmetric operator $S$ which has no $\\mathfrak{U}$-invariant self-adjoint extensions. It was discovered that such symmetric operator has a constant characteristic function \\cite{KO}. For this reason, each symmetric operator $S$ with constant characteristic function is called a \\emph{Phillips "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04915","kind":"arxiv","version":2},"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"}