{"paper":{"title":"The spectra of harmonic layer potential operators on domains with rotationally symmetric conical points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.AP","authors_text":"Johan Helsing, Karl-Mikael Perfekt","submitted_at":"2017-03-05T17:12:23Z","abstract_excerpt":"We study the adjoint of the double layer potential associated with the Laplacian (the adjoint of the Neumann-Poincar\\'e operator), as a map on the boundary surface $\\Gamma$ of a domain in $\\mathbb{R}^3$ with conical points. The spectrum of this operator directly reflects the well-posedness of related transmission problems across $\\Gamma$. In particular, if the domain is understood as an inclusion with complex permittivity $\\epsilon$, embedded in a background medium with unit permittivity, then the polarizability tensor of the domain is well-defined when $(\\epsilon+1)/(\\epsilon-1)$ belongs to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01628","kind":"arxiv","version":2},"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"}