{"paper":{"title":"On invariant measures associated to weakly coupled systems of Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Davide Addona, Luca Lorenzi, Luciana Angiuli","submitted_at":"2017-05-10T14:06:15Z","abstract_excerpt":"In this paper, we deal with weakly coupled elliptic systems $\\boldsymbol{\\mathcal A}$ with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the semigroup $({\\bf T}(t))_{t\\ge 0}$ associated to $\\boldsymbol{\\mathcal A}$ in $C_b(\\mathbb R^d;\\mathbb R^m)$. We also show some relevant properties of the extension of $({\\bf T}(t))_{t\\ge 0}$ to the $L^p$-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of $({\\bf T}(t))_{t\\ge 0}$ as $t$ tends to $+\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03784","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"}