{"paper":{"title":"Clark measures on the complex sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Aleksei B. Aleksandrov, Evgueni Doubtsov","submitted_at":"2019-04-08T19:18:41Z","abstract_excerpt":"Let $B_d$ denote the unit ball of $\\mathbb{C}^d$, $d\\ge 1$. Given a holomorphic function $\\varphi: B_d \\to B_1$, we study the corresponding family $\\sigma_\\alpha[\\varphi]$, $\\alpha\\in\\partial B_1$, of Clark measures on the unit sphere $\\partial B_d$. If $\\varphi$ is an inner function, then we introduce and investigate related unitary operators $U_\\alpha$ mapping analogs of model spaces onto $L^2(\\sigma_\\alpha)$, $\\alpha\\in\\partial B_1$. In particular, we explicitly characterize the set of $U_\\alpha^* f$ such that $f\\sigma_\\alpha$ is a pluriharmonic measure. Also, for an arbitrary holomorphic $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04308","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"}