{"paper":{"title":"Aliasing and oblique dual pair designs for consistent sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Demetrio Stojanoff, Maria Jose Benac, Pedro Massey","submitted_at":"2014-10-10T15:33:52Z","abstract_excerpt":"In this paper we study some aspects of oblique duality between finite sequences of vectors $\\cF$ and $\\cG$ lying in finite dimensional subspaces $\\cW$ and $\\cV$, respectively. We compute the possible eigenvalue lists of the frame operators of oblique duals to $\\cF$ lying in $\\cV$; we then compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for $\\cF$ under some restrictions. We obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces $\\cV$ and $\\cW$ has in oblique duality. We apply this analysis to c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2809","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"}