{"paper":{"title":"A Characterization of Multivariate Gaussian Weyl--Heisenberg Frames, (II)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP","math.SG","quant-ph"],"primary_cat":"math-ph","authors_text":"Maurice de Gosson","submitted_at":"2010-12-02T18:14:44Z","abstract_excerpt":"In a previous Note we established a necessary and sufficient condition for a multivariate Weyl--Heisenberg system G({\\phi},{\\Lambda}) to be a frame when the window is a generalized Gaussian (squeezed coherent state) and {\\Lambda} a rectangular lattice. In this Note we extend this result to lattices of the type ${\\Lambda}=MZ^{2n}$ where M is a positive definite symmetric matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0528","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"}