{"paper":{"title":"A Family of Circular Bargmann Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Zouhair Mouayn","submitted_at":"2011-05-22T16:54:19Z","abstract_excerpt":"When considering a charged particle evolving in the Poincar\\'e disk under influence of a uniform magnetic field with a strength proportional to +1, we construct for all hyperbolic Landau level \\epsilon^\\gamma_$m$ m = 4m(-m), m 2 Z+ \\[0, /2] a family of coherent states transforms labeled by (,m) and mapping isometrically square integrable functions on the unit circle with respect to the measure sin^\\gamma-2m (\\theta/2) d\\theta onto spaces of bound states of the particle. These transforms are called circular Bargmann transforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4350","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"}