{"paper":{"title":"On the generation of groups of bounded linear operators on Fr\\'{e}chet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alex Pereira da Silva, \\'Eder R\\'itis Arag\\~ao Costa","submitted_at":"2017-03-03T18:43:54Z","abstract_excerpt":"In this paper we present a general method for generation of uniformly continuous groups on abstract Fr\\'{e}chet spaces (without appealing to spectral theory) and apply it to a such space of distributions, namely ${\\mathscr F}L^{2}_{loc}(\\mathbb{R}^{n})$, so that the linear evolution problem \\begin{equation*} \\left\\{\\begin{array}{l} u_{t} = a(D)u, t \\in \\mathbb{R} \\\\ u(0) = u_0 \\end{array} \\right. \\end{equation*}always has a unique solution in such a space, for every pseudodifferential operator $a(D)$ with constant coefficients. We also provide necessary and sufficient conditions so that the sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01283","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"}