{"paper":{"title":"Conic stability of polynomials and positive maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Papri Dey, Stephan Gardoll, Thorsten Theobald","submitted_at":"2019-08-29T09:40:01Z","abstract_excerpt":"Given a proper cone $K \\subseteq \\mathbb{R}^n$, a multivariate polynomial $f \\in \\mathbb{C}[z] = \\mathbb{C}[z_1, \\ldots, z_n]$ is called $K$-stable if it does not have a root whose vector of the imaginary parts is contained in the interior of $K$. If $K$ is the non-negative orthant, then $K$-stability specializes to the usual notion of stability of polynomials.\n  We study conditions and certificates for the $K$-stability of a given polynomial $f$, especially for the case of determinantal polynomials as well as for quadratic polynomials. A particular focus is on psd-stability. For cones $K$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11124","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.11124/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"}