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Under the assumption that A(0) is a selfadjoint operator which can be of infinite rank, we study the distribution near the origin of the characteristic values of 1-K(z), i.e. the complex numbers w for which the operator 1-K(w) is not invertible, and we show that generically the characteristic values of 1-K(z) converge to 0 with the same rate as the eigenvalues of A(0).\n  We apply our abstract results "},"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":"1109.3985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-19T09:54:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f84fd8a8edd779aa9826a2c62bf83c8c966f01305022edaf1a4474a29ce6f4ff","abstract_canon_sha256":"a5a296d67d2340946b8b73ebb3fdcccaa5ce540882d2f7c76e35b8b035fa2123"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:45.413496Z","signature_b64":"+UNLTijHDtdSwggfdn0FLIXKzIrEW39KovfPLFgsmWsGj+ZdASR5TJNjyjhB/Q0zHwNsy+0op6B2+1N5mtdYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7742c44b1424a09cee246babe861f4fa943388c6b857a3e7d55c6584b536fd00","last_reissued_at":"2026-05-18T04:12:45.412864Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:45.412864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting function of characteristic values and magnetic resonances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Raikov, Jean-Francois Bony, Vincent Bruneau","submitted_at":"2011-09-19T09:54:05Z","abstract_excerpt":"We consider the meromorphic operator-valued function 1-K(z) = 1-A(z)/z where A(z) is holomorphic on the domain D, and has values in the class of compact operators acting in a given Hilbert space. 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