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Consequently we determine all the self-adjoint realizations of $H$ in terms of the behaviour of the functions of their domain in the origin. When $\\sup_{x} |x||\\mathbb V(x)| \\leq 1$, we discuss the problem of selecting the distinguished extension requiring that its domain is included in the domain of the appro"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.01659","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-03T09:49:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"43b36477e9ce566119dbb35cb175f110d1cd7730f153d70121df154fb5e2f869","abstract_canon_sha256":"0cb8bc3fbf6913d2ae2e984a13dd582d78425ad9cdb3830a1333ca495fbf77bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:30.086150Z","signature_b64":"JLvYW9HrMYi3zKfxP8icApc5QTSqUPfprpoXnztpaASsyst5rkc16Y8V+9sclaV87nhkXeqlQ6iGz5GMBOJLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bd17c989e95f0d4893d3a17468f5e0d801c5803fcbac2a28a353192f15fa3f9","last_reissued_at":"2026-05-17T23:47:30.085595Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:30.085595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Biagio Cassano, Fabio Pizzichillo","submitted_at":"2018-10-03T09:49:31Z","abstract_excerpt":"We determine explicitly a boundary triple for the Dirac operator $H:=-i\\alpha\\cdot \\nabla + m\\beta + \\mathbb V(x)$ in $\\mathbb R^3$, for $m\\in\\mathbb R$ and $\\mathbb V(x)= |x|^{-1} ( \\nu \\mathbb{I}_4 +\\mu \\beta -i \\lambda \\alpha\\cdot{x}/|x|\\,\\beta)$, with $\\nu,\\mu,\\lambda \\in \\mathbb R$. Consequently we determine all the self-adjoint realizations of $H$ in terms of the behaviour of the functions of their domain in the origin. 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