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We investigate the absolutely continuous parts of different self-adjoint realizations of $\\mathcal{A}$. In particular, we show that Dirichlet and Neumann realizations, $A^D$ and $A^N$, are absolutely continuous and unitary equivalent to each other and to the absolutely continuous part of the Krein realization. Moreover, if $\\inf\\sigma_{ess}(T) = \\inf\\sigma(T) \\g"},"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":"1102.3849","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-18T14:56:46Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"61822e952b6e312ab19cdad61e342ee847341a0fcc44bf16ec718bb2659bfbcb","abstract_canon_sha256":"c159368bfbd070d42b581506de7a573690b0cbf4c680eefe2040a39f400afda9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:10.184690Z","signature_b64":"V8vGDmgEexE1j346v2l4v2Ds1k8KNfrL3tyvZRIm/gmyrgQIzERv6zhnL9BmY0N1PLIURV+v04BWLwcUfrD4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca49c7cec957a1585652a2eb57aacf92afd201e2af9924968baec4f45c753195","last_reissued_at":"2026-05-18T04:22:10.184247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:10.184247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sturm-Liouville boundary value problems with operator potentials and unitary equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Hagen Neidhardt, Mark Malamud","submitted_at":"2011-02-18T14:56:46Z","abstract_excerpt":"Consider the minimal Sturm-Liouville operator $A = A_{\\rm min}$ generated by the differential expression $\\mathcal{A} := -\\frac{d^2}{dt^2} + T$ in the Hilbert space $L^2(\\mathbb{R}_+,\\mathcal{H})$ where $T = T^*\\ge 0$ in $\\mathcal{H}$. We investigate the absolutely continuous parts of different self-adjoint realizations of $\\mathcal{A}$. In particular, we show that Dirichlet and Neumann realizations, $A^D$ and $A^N$, are absolutely continuous and unitary equivalent to each other and to the absolutely continuous part of the Krein realization. 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