{"paper":{"title":"Szego limit theorem on the lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jitendriya Swain, M. Krishna","submitted_at":"2011-02-21T04:53:01Z","abstract_excerpt":"In this paper, we prove a Szeg\\\"{o} type limit theorem on $\\ell^2(\\ZZ^d)$. We consider operators of the form $H=\\Delta+V$, $V$ multiplication by a positive sequence $\\{V(n), n \\in \\ZZ^d\\}$ with $V(n) \\rightarrow \\infty, |n| \\rightarrow \\infty $\non $\\ell^2(\\ZZ^d)$ and $\\pi_{\\lambda}$ the orthogonal projection of $\\ell^2(\\mathbb{Z}^d)$ on to the space of eigenfunctions of $H$ with eigenvalues $\\leq \\lambda$. We take $B$ to be a pseudo difference operator of order zero with symbol $b(x,n), (x,n) \\in \\TT^d\\times \\ZZ^d$ and show that for nice functions $f$ $$ \\lim_{\\lambda \\rightarrow \\infty} Tr(f("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4131","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"}