{"paper":{"title":"Pairs of Clark Unitary Operators on the Bidisk and their Taylor Joint Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Alan Sola, Constanze Liaw, Kelly Bickel, Palak Arora","submitted_at":"2025-11-07T15:06:14Z","abstract_excerpt":"We develop a Clark theory for commuting compressed shift operators on model spaces $K_{\\phi}$ associated with inner functions $\\phi$ on the bidisk, which exhibits both similarities and marked differences compared to the classical one-variable version. We first identify the adjoint of the embedding operator $J_{\\alpha} \\colon K_{\\phi}\\to L^2(\\sigma_{\\alpha})$ as a weighted Cauchy transform of the Clark measure $\\sigma_{\\alpha}$. Under natural assumptions, which generically include the case when $\\phi$ is rational inner, we obtain commuting unitaries on $K_{\\phi}$ that are (often infinite-dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.05306","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.05306/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}