{"paper":{"title":"Eigenfunctions of Composition Operators on Bloch-type Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bhupendra Paudyal","submitted_at":"2017-06-15T12:12:36Z","abstract_excerpt":"Suppose $\\varphi$ is a holomorphic self map of the unit disk and $C_\\varphi$ is a composition operator with symbol $\\varphi$ that fixes the origin and $0<|\\varphi'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic solutions of Schr\\\"oder equation for the composition operator $C_\\varphi$ belong to a Bloch-type space $\\mathcal{B}_\\alpha$ for some $\\alpha>0$. The results from composition operators have been extended to weighted composition operators in the second part of this work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04833","kind":"arxiv","version":2},"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"}