Von Neumann algebras and

linear independence of translates

Author:
Peter A. Linnell

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3269-3277

MSC (1991):
Primary 46L10; Secondary 42C99

DOI:
https://doi.org/10.1090/S0002-9939-99-05102-3

Published electronically:
May 4, 1999

MathSciNet review:
1637388

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Abstract | References | Similar Articles | Additional Information

Abstract: For and , define and if , 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 , 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 .

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Additional Information

**Peter A. Linnell**

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

Email:
linnell@math.vt.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05102-3

Keywords:
Group von Neumann algebra,
Gabor analysis,
Heisenberg group

Received by editor(s):
January 30, 1998

Published electronically:
May 4, 1999

Communicated by:
David R. Larson

Article copyright:
© Copyright 1999
American Mathematical Society