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Kutsenko","submitted_at":"2015-10-20T14:17:55Z","abstract_excerpt":"As it is shown in previous works, discrete periodic operators with defects are unitarily equivalent to the operators of the form $$\n  {\\mathcal A}{\\bf u}={\\bf A}_0{\\bf u}+{\\bf A}_1\\int_0^1dk_1{\\bf B}_1{\\bf\n  u}+...+{\\bf A}_N\\int_0^1dk_1...\\int_0^1dk_N{\\bf B}_N{\\bf u},\\ \\ {\\bf\n  u}\\in L^2([0,1]^N,\\mathbb{C}^M), $$ where $({\\bf A},{\\bf B})(k_1,...,k_N)$ are continuous matrix-valued functions of appropriate sizes. All such operators form a non-closed algebra ${\\mathscr H}_{N,M}$. In this article we show that there exist a trace $\\pmb{\\tau}$ and a determinant $\\pmb{\\pi}$ defined for operators from"},"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":"1510.05906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-10-20T14:17:55Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f19a1e645f6c4a770c4133374b823914fb75020a0974a6843fc4a6209a30ffaf","abstract_canon_sha256":"cf24e037f29c0c88e130f3534761759df19ff306a2c6225f845fd976a1468c95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:20.299325Z","signature_b64":"t2CC07BTR8zXhmUnzKuyJtCoqij+3598abVIaG9jqOkrCvURaiQ+JjxzXvgcZFJ4m27Ls4l40k5EUC7ojV/rAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38e144f7c427e42192768c6d76680627c9669497497db03c11bd08180eb29ceb","last_reissued_at":"2026-05-18T01:29:20.298666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:20.298666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determinants and traces of multidimensional discrete periodic operators with defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Anton A. 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