{"paper":{"title":"Essential self-adjointness, generalized eigenforms, and spectra for the $\\bar\\partial$-Neumann problem on $G$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.SP","authors_text":"Joe J. Perez, Peter Stollmann","submitted_at":"2011-01-10T16:11:13Z","abstract_excerpt":"Let $M$ be a strongly pseudoconvex complex manifold which is also the total space of a principal $G$-bundle with $G$ a Lie group and compact orbit space $\\bar M/G$. Here we investigate the $\\bar\\partial$-Neumann Laplacian on $M$. We show that it is essentially self-adjoint on its restriction to compactly supported smooth forms. Moreover we relate its spectrum to the existence of generalized eigenforms: an energy belongs to $\\sigma(\\square)$ if there is a subexponentially bounded generalized eigenform for this energy. Vice versa, there is an expansion in terms of these well-behaved eigenforms s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1863","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":""},"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"}