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It is assumed that the homogeneous part is strongly propagative. In the nonhomegeneous case it is assumed that the operator is isotropic . The spectral theory of such systems and their potential perturbations is expounded, and a Limiting Absorption Principle is obtained up to thresholds. Special attention is given to a detailed study of the Dirac and Maxwell operators.\n  The estimate"},"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":"1902.03010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-08T10:34:27Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"b0272660342a6dcfa766bb439db2f74152536f6d172b0afb637c66ec525ce68f","abstract_canon_sha256":"641e466acabcf940684945187093f817aacf0c46db4ce059e9c350bb5d6d3cb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:28.588968Z","signature_b64":"0K25dOo+KQVsB/fMjZapy0qdOdlZpfvIoUduOFOTMKxsj96FE3nUugReJ0yNIJshZd7F9haQwlW90OZB0tOABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"221041dda8411d579b2e562a329e77834bdec369479c8b1b26e889397f724261","last_reissued_at":"2026-05-17T23:54:28.588245Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:28.588245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral theory of first-order systems: from crystals to Dirac operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Matania Ben-Artzi, Tomio Umeda","submitted_at":"2019-02-08T10:34:27Z","abstract_excerpt":"Let\n  $$L_0=\\suml_{j=1}^nM_j^0D_j+M_0^0,\\,\\,\\,\\,D_j=\\frac{1}{i}\\frac{\\pa}{\\paxj},\n  \\quad x\\in\\Rn,$$\n  be a constant coefficient\n  first-order partial differential system, where the matrices $M_j^0$ are Hermitian. It is assumed that the homogeneous part is strongly propagative. In the nonhomegeneous case it is assumed that the operator is isotropic . The spectral theory of such systems and their potential perturbations is expounded, and a Limiting Absorption Principle is obtained up to thresholds. 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