{"paper":{"title":"Manifolds of Hilbert space projections","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.FA","authors_text":"Rupert H. Levene, Stephen C. Power","submitted_at":"2007-09-13T16:49:54Z","abstract_excerpt":"The Hardy space H^2(R) for the upper half plane together with a unimodular function group representation u(\\lambda) = \\exp(i(\\lambda_1\\psi_1 + ... + \\lambda_n\\psi_n)) for \\lambda in R^n, gives rise to a manifold M of orthogonal projections for the subspaces u(\\lambda)H^2(R) of L^2(R). For classes of admissible functions \\psi_i the strong operator topology closures of M and M \\cup M^\\perp are determined explicitly as various n-balls and n-spheres. The arguments used are direct and rely on the analysis of oscillatory integrals and Hilbert space geometry. Some classes of these closed projection m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2117","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"}