{"paper":{"title":"Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.SP"],"primary_cat":"math.NA","authors_text":"Martin Halla","submitted_at":"2019-08-14T09:09:20Z","abstract_excerpt":"We consider Galerkin approximations of holomorphic Fredholm operator eigenvalue problems for which the operator values don't have the structure \"coercive+compact\". In this case the regularity (in sense of [O. Karma, Numer. Funct. Anal. Optim. 17 (1996)]) of Galerkin approximations is not unconditionally satisfied and the question of convergence is delicate. We report a technique to prove regularity of approximations which is applicable to a wide range of eigenvalue problems. In particular, we introduce the concepts of weak T-coercivity and T-compatibility and prove that for weakly T-coercive o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05029","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05029/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}