{"paper":{"title":"On compressions of self-adjoint extensions of a symmetric linear relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Vadim Mogilevskii","submitted_at":"2018-12-01T13:24:18Z","abstract_excerpt":"Let $A$ be a symmetric linear relation in the Hilbert space $\\gH$ with equal deficiency indices $n_\\pm (A)\\leq\\infty$. A self-adjoint linear relation $\\wt A\\supset A$ in some Hilbert space $\\wt\\gH\\supset \\gH$ is called an exit space extension of $A$; such an extension is called finite-codimensional if $\\dim (\\wt\\gH\\ominus\\gH)< \\infty$. We study the compressions $C (\\wt A)=P_\\gH\\wt A\\up\\gH$ of exit space extensions $\\wt A=\\wt A^*$. For a certain class of extensions $\\wt A$ we parameterize the compressions $C (\\wt A)$ by means of abstract boundary conditions. This enables us to characterize vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00204","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":""},"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"}