{"paper":{"title":"Construction of concrete orthonormal basis for (L^2,\\Gamma,\\chi)-theta functions associated to discrete subgroups of rank one in (C,+)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.CV","authors_text":"Ahmed Intissar, Allal Ghanmi","submitted_at":"2012-12-09T09:41:49Z","abstract_excerpt":"Let \\chi be a character on a discrete subgroup \\Gamma of rank one of the additive group (C,+). We construct a complete orthonormal basis of the Hilbert space of (L^2,\\Gamma,\\chi)-theta functions. Furthermore, we show that it possesses a Hilbertian orthogonal decomposition involving the L^2-eigenspaces of the Landau operator \\Delta_\\nu; \\nu>0, associated to the eigenvalues \\nu m. For m=0, the associated L^2-eigenspace is the Hilbert subspace of entire (L^2,\\Gamma,\\chi)-theta functions. Corresponding orthonormal basis are constructed and the corresponding reproducing kernel can be expressed in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1870","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"}