Manifold structure of spaces of spherical tight frames
| dc.creator | Dykema, Ken | |
| dc.creator | Strawn, Nate | |
| dc.date | 2003-07-28 | |
| dc.date | 2003-09-28 | |
| dc.date.accessioned | 2026-07-07T04:59:56Z | |
| dc.date.available | 2026-07-07T04:59:56Z | |
| dc.description | We consider the space F^E_{k,n} of all spherical tight frames of k vectors in real or complex n--dimensional Hilbert space E^n, i.e. E=R or E=C, and its orbit space G^E_{k,n}=F^E_{k,n}/O^E_n under the obvious action of the group O^E_n of structure preserving transformations of E^n. We show that the quotient map F^E_{k,n} -> G^E_{k,n} is a locally trivial fiber bundle (also in the more general case of ellipsoidal tight frames) and that there is a homeomorphism G^E_{k,n} -> G^E_{k,k-n}. We show that G^E_{k,n} and F^E_{k,n} are real manifolds whenever k and n are relatively prime, and we describe them as disjoint unions of finitely many manifolds (of various dimensions) when when k and n have a common divisor. We also prove that F^R_{k,2} is connected (k >= 4) and F^R_{n+2,n} is connected, (n >= 2). The spaces G^R_{4,2} and G^R_{5,2} are investigated in detail. The former is found to be a graph and the latter is the orientable surface of genus 25. | |
| dc.description | The new version corrects some typographical errors, including a misleading error in the abstract: we show connectedness of F^R_{k,2}, not of more general F^R_{k,n} | |
| dc.identifier | https://arxiv.org/abs/math/0307367 | |
| dc.identifier | http://arxiv.org/abs/math/0307367 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68192 | |
| dc.subject | Functional Analysis | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Operator Algebras | |
| dc.subject | 42C15; 94A12; 14P05 | |
| dc.title | Manifold structure of spaces of spherical tight frames | |
| dc.type | text |