{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05906","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}