Von Neumann algebras and linear independence of translates
| dc.creator | Linnell, Peter A. | |
| dc.date | 1998-07-11 | |
| dc.date.accessioned | 2026-07-07T05:25:22Z | |
| dc.date.available | 2026-07-07T05:25:22Z | |
| dc.description | For x,y in R (where R denotes the real numbers) and f in L^2(R), define (x,y)f(t) = e^{2 pi i yt}f(t+x) and if L is a subset of R^2, define S(f,L) = {(x,y)f | (x,y) in L}. It has been conjectured that if f is not 0, then S(f,L) is linearly independent over C; one motivation for this problem comes from Gabor analysis. We shall prove that S(f,L) is linearly independent if f is nonzero and L is contained in a discrete subgroup of R^2, and as a byproduct we shall obtain some results on the group von Neumann algebra generated by the operators {(x,y) | (x,y) in L}. Also we shall prove these results for the obvious generalization to R^n. | |
| dc.description | 9 pages, AMS-LaTeX, Proc. Amer. Math. Soc. to appear | |
| dc.identifier | https://arxiv.org/abs/math/9807057 | |
| dc.identifier | http://arxiv.org/abs/math/9807057 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77148 | |
| dc.subject | Representation Theory | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L10; 42C99 | |
| dc.title | Von Neumann algebras and linear independence of translates | |
| dc.type | text |