{"paper":{"title":"Frames of translates with prescribed fine structure in shift invariant spaces","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":"2015-12-22T15:26:39Z","abstract_excerpt":"For a given finitely generated shift invariant (FSI) subspace $\\cW\\subset L^2(\\R^k)$ we obtain a simple criterion for the existence of shift generated (SG) Bessel sequences $E(\\cF)$ induced by finite sequences of vectors $\\cF\\in \\cW^n$ that have a prescribed fine structure i.e., such that the norms of the vectors in $\\cF$ and the spectra of $S_{E(\\cF)}$ is prescribed in each fiber of $\\text{Spec}(\\cW)\\subset \\T^k$. We complement this result by developing an analogue of the so-called sequences of eigensteps from finite frame theory in the context of SG Bessel sequences, that allows for a detail"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07122","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"}