{"paper":{"title":"Resonances and residue operators for pseudo-Riemannian hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.SP","authors_text":"Jan Frahm, Polyxeni Spilioti","submitted_at":"2023-03-08T18:24:51Z","abstract_excerpt":"For any pseudo-Riemannian hyperbolic space $X$ over $\\mathbb{R},\\mathbb{C},\\mathbb{H}$ or $\\mathbb{O}$, we show that the resolvent $R(z)=(\\Box-z\\operatorname{Id})^{-1}$ of the Laplace-Beltrami operator $-\\Box$ on $X$ can be extended meromorphically across the spectrum of $\\Box$ as a family of operators $C_c^\\infty(X)\\to \\mathcal{D}'(X)$. Its poles are called resonances and we determine them explicitly in all cases. For each resonance, the image of the corresponding residue operator in $\\mathcal{D}'(X)$ forms a representation of the isometry group of $X$, which we identify with a subrepresentat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.04780","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/2303.04780/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"}