{"paper":{"title":"Bohl-Perron type stability theorems for linear difference equations with infinite delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Elena Braverman, Illya M. Karabash","submitted_at":"2010-09-30T15:10:45Z","abstract_excerpt":"Relation between two properties of linear difference equations with infinite delay is investigated: (i) exponential stability, (ii) $\\l^p$-input $\\l^q$-state stability (sometimes is called Perron's property). The latter means that solutions of the non-homogeneous equation with zero initial data belong to $\\l^q$ when non-homogeneous terms are in $\\l^p$. It is assumed that at each moment the prehistory (the sequence of preceding states) belongs to some weighted $\\l^r$-space with an exponentially fading weight (the phase space). Our main result states that (i) $\\Leftrightarrow$ (ii) whenever $(p,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6163","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"}