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In this paper we consider the compact approximations $D_\\varepsilon(\\lambda)$ of $D(\\lambda)$, given by $$D_\\varepsilon(\\lambda)=\\psi_\\varepsilon(H-\\lambda)-\\psi_\\varepsilon(H_0-\\la"},"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":"1409.1728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-09-05T10:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"a3949038147b6d887f32049f9291a9c09a8de1b0e3aea1e89bbba0bd4605e90c","abstract_canon_sha256":"4a4d035cf6e31d8c371805ce17aa2344eeb7c3ff521bb8bf4756f093aa5111eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:32.522163Z","signature_b64":"1lKIcQDIz6CQ1K6AoS5CmNDns42h+UGocwSubvb5uSoXT4/WZ25tBpSg0pfVmWvzGMXhvq9xaKPl0EZLvhq4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2da9dca7d4539febf3b7d0c052eb1f9f690b2b73087d25885f0eae147762629a","last_reissued_at":"2026-05-18T02:25:32.521687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:32.521687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The spectral density of a difference of spectral projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski","submitted_at":"2014-09-05T10:23:07Z","abstract_excerpt":"Let $H_0$ and $H$ be a pair of self-adjoint operators satisfying some standard assumptions of scattering theory. 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