{"paper":{"title":"The spectral density of a product of spectral projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Rupert L. Frank","submitted_at":"2014-09-03T19:40:55Z","abstract_excerpt":"We consider the product of spectral projections $$ \\Pi_\\epsilon(\\lambda) = 1_{(-\\infty,\\lambda-\\epsilon)}(H_0) 1_{(\\lambda+\\epsilon,\\infty)}(H) 1_{(-\\infty,\\lambda-\\epsilon)}(H_0) $$ where $H_0$ and $H$ are the free and the perturbed Schr\\\"odinger operators with a short range potential, $\\lambda>0$ is fixed and $\\epsilon\\to0$. We compute the leading term of the asymptotics of $\\mathrm{Tr}\\ f(\\Pi_\\epsilon(\\lambda))$ as $\\epsilon\\to0$ for continuous functions $f$ vanishing sufficiently fast near zero. Our construction elucidates calculations that appeared earlier in the theory of \"Anderson's ort"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1206","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"}