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We show that the spectral properties of the operators depend crucially on the one-dimensional Schr\\\"{o}dinger operators $L= -\\frac{"},"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":"1708.07375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-08-24T12:32:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5096507efcb1a8487273c35e0938f596e1da7578d3efee71f3425cbda94e2c71","abstract_canon_sha256":"168a77b6f7c3f1471b6becb1921bdc07ba7342bde47e6e23a488fd132cf3b73c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:00.417437Z","signature_b64":"REVVp9ld7YWdU2J7D9KkYPMpW1G+/WKsah07hYZdENBebZ/tiOBNzLTXDmsKENHZ2bbjeEkADeXQmNa1fZjvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"340cce7edf0604cdd6b7ff269ee2968ee20a233dd9a45a3469e4ee94b3e9e416","last_reissued_at":"2026-05-18T00:30:00.416724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:00.416724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A magnetic version of the Smilansky-Solomyak model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Diana Barseghyan, Pavel Exner","submitted_at":"2017-08-24T12:32:22Z","abstract_excerpt":"We analyze spectral properties of two mutually related families of magnetic Schr\\\"{o}dinger operators, $H_{\\mathrm{Sm}}(A)=(i \\nabla +A)^2+\\omega^2 y^2+\\lambda y \\delta(x)$ and $H(A)=(i \\nabla +A)^2+\\omega^2 y^2+ \\lambda y^2 V(x y)$ in $L^2(R^2)$, with the parameters $\\omega>0$ and $\\lambda<0$, where $A$ is a vector potential corresponding to a homogeneous magnetic field perpendicular to the plane and $V$ is a regular nonnegative and compactly supported potential. 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