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Vesalainen","submitted_at":"2013-05-28T17:54:49Z","abstract_excerpt":"Let $\\Omega\\subseteq\\mathbb R^n$ be a non-empty open set for which the Sobolev embedding $H_0^2(\\Omega)\\longrightarrow L^2(\\Omega)$ is compact, and let $V\\in L^\\infty(\\Omega)$ be a potential taking only positive real values and satisfying the asymptotics $V(\\cdot)\\asymp\\left\\langle\\cdot\\right\\rangle^{-\\alpha}$ for some $\\alpha\\in\\left]3,\\infty\\right[$. We establish the discreteness of the set of real transmission eigenvalues for both Schr\\\"odinger and Helmholtz scattering with these potentials."},"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":"1305.6571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-28T17:54:49Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"2aee092efc93b24deb6e5f65a03371165b0d87b3d23922a2fa73bbf22ca20477","abstract_canon_sha256":"89bb6e3d275e9f6dfca7f8df0041d93b54451da46a74fe6220bcc3045e632398"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:46.498775Z","signature_b64":"m/cw5gzyKwFMBQRMntVdKcGhzBCxfxNOdJ+m+kSVyh9ACGs0PT2pOn68lUAWsUUmtF1UEH/wA6M8kO3W2BuuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfec9716ac547630710abe00e5127f1476f7986d9fb82370bd7fc8a2ac9eaa77","last_reissued_at":"2026-05-18T03:01:46.498229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:46.498229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transmission Eigenvalues for a Class of Non-Compactly Supported Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Esa V. 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