{"paper":{"title":"On Parseval frames of exponentially decaying composite Wannier functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"David Auckly, Peter Kuchment","submitted_at":"2017-04-19T13:39:57Z","abstract_excerpt":"Let $L$ be a periodic self-adjoint linear elliptic operator in $\\R^n$ with coefficients periodic with respect to a lattice $\\G$, e.g. Schr\\\"{o}dinger operator $(i^{-1}\\partial/\\partial_x-A(x))^2+V(x)$ with periodic magnetic and electric potentials $A,V$, or a Maxwell operator $\\nabla\\times\\varepsilon (x)^{-1}\\nabla\\times$ in a periodic medium. Let also $S$ be a finite part of its spectrum separated by gaps from the rest of the spectrum. We address here the question of existence of a finite set of exponentially decaying Wannier functions $w_j(x)$ such that their $\\G$-shifts $w_{j,\\g}(x)=w_j(x-\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05728","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"}