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In L 2 ($\\Omega$, {\\lambda}), $\\delta$ = d * and D is self-adjoint, thus having bounded resolvents (I + itD) --1 t$\\in$R as well as a bounded functional calculus in L 2 ($\\Omega$, {\\lambda}). We inve"},"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":"1608.01797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-05T08:20:06Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"55e597b779fcce81173eb142aec0c51a17e9d44698b82adf5b916008f0d49cc7","abstract_canon_sha256":"44f429c3880ff7331c25e00e924cdb23a9fd63347b57ad3342bdefa1a78bd09d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:44.574846Z","signature_b64":"CjWLuBfw1hXEnICJy6Ym2pLRm9RontzH+oZST22l2/qaE5SIHRNvE34SWRRAh72zyYQ+CxQsp3H+I3EnIPnHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a44458b89580d96f087ec946265e4b7bc0de67ff5121242d41abc00b9973070","last_reissued_at":"2026-05-18T01:09:44.574173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:44.574173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hodge-Dirac, Hodge-Laplacian and Hodge-Stokes operators in L^p spaces on Lipschitz domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Alan Mcintosh (MSI), Sylvie Monniaux (I2M)","submitted_at":"2016-08-05T08:20:06Z","abstract_excerpt":"This paper concerns Hodge-Dirac operators D = d + $\\delta$ acting in L p ($\\Omega$, {\\lambda}) where $\\Omega$ is a bounded open subset of R n satisfying some kind of Lipschitz condition, {\\lambda} is the exterior algebra of R n , d is the exterior derivative acting on the de Rham complex of differential forms on $\\Omega$, and $\\delta$ is the interior derivative with tangential boundary conditions. In L 2 ($\\Omega$, {\\lambda}), $\\delta$ = d * and D is self-adjoint, thus having bounded resolvents (I + itD) --1 t$\\in$R as well as a bounded functional calculus in L 2 ($\\Omega$, {\\lambda}). 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