{"paper":{"title":"Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Jorge Antezana, Maria Guadalupe Garcia","submitted_at":"2019-07-20T22:58:43Z","abstract_excerpt":"Let $\\mu$ be a probability measure on $\\mathbb{T}$ that is singular with respect to the Haar measure. In this paper we study Fourier expansions in $L^2(\\mathbb{T},\\mu)$ using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials $\\{z^n\\}_{n\\in \\mathbb{N}}$ is effective in $L^2(\\mathbb{T},\\mu)$, it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame $P_\\varphi(z^n)$ for the model subspace $\\mathcal{H}(\\varphi)= H^2 \\ominus \\varphi H^2$, where $P_\\varp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08876","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"}