{"paper":{"title":"Integral operators on the Oshima compactification of a Riemannian symmetric space of non-compact type. Microlocal analysis and kernel asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aprameyan Parthasarathy, Pablo Ramacher","submitted_at":"2011-02-24T19:28:46Z","abstract_excerpt":"Let $\\X\\simeq G/K$ be a Riemannian symmetric space of non-compact type, $\\widetilde \\X$ its Oshima compactification, and $(\\pi,\\mathrm{C}(\\widetilde \\X))$ the regular representation of $G$ on $\\widetilde \\X$. We study integral operators on $\\widetilde \\X$ of the form $\\pi(f)$, where $f$ is a rapidly falling function on $G$, and characterize them within the framework of pseudodifferential operators, describing the singular nature of their kernels. In particular, we consider the holomorphic semigroup generated by a strongly elliptic operator associated to the representation $\\pi$, as well as its"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5069","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"}