{"paper":{"title":"A note on the quantization error for in-homogeneous self-similar measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Sanguo Zhu","submitted_at":"2016-08-31T05:37:12Z","abstract_excerpt":"We further study the asymptotics of quantization errors for two classes of in-homogeneous self-similar measures $\\mu$. We give a new sufficient condition for the upper quantization coefficient for $\\mu$ to be finite. This, together with our previous work, leads to a necessary and sufficient condition for the upper and lower quantization coefficient of $\\mu$ to be both positive and finite. Furthermore, we determine (estimate) the convergence order of the quantization error in case that the quantization coefficient is infinite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08732","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"}