Von Neumann algebras and linear independence of translates期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Von Neumann algebras and linear independence of translates

Authors:	Peter A. Linnell

Affiliation:	Department of Mathematics, Virginia Polytech Institute and State University, Blacksburg, Virginia 24061--0123

Abstract:	For and $f in L^2(mathbb {R})$ , define $(x,y) f(t) = e^{2pi iyt} f(t+x)$ and if $Lambda subseteq mathbb {R}^2$ , define . It has been conjectured that if , then is linearly independent over ; one motivation for this problem comes from Gabor analysis. We shall prove that is linearly independent if and is contained in a discrete subgroup of $mathbb {R}^2$ , and as a byproduct we shall obtain some results on the group von Neumann algebra generated by the operators . Also, we shall prove these results for the obvious generalization to $mathbb {R}^n$ .

Keywords:	Group von Neumann algebra Gabor analysis Heisenberg group

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