Open Access
October 2017 Linear dependency of translations and square-integrable representations
Peter A. Linnell, Michael J. Puls, Ahmed Roman
Banach J. Math. Anal. 11(4): 945-962 (October 2017). DOI: 10.1215/17358787-2017-0028


Let G be a locally compact group. We examine the problem of determining when nonzero functions in L2(G) have linearly independent left translations. In particular, we establish some results for the case when G has an irreducible, square-integrable, unitary representation. We apply these results to the special cases of the affine group, the shearlet group, and the Weyl–Heisenberg group. We also investigate the case when G has an abelian, closed subgroup of finite index.


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Peter A. Linnell. Michael J. Puls. Ahmed Roman. "Linear dependency of translations and square-integrable representations." Banach J. Math. Anal. 11 (4) 945 - 962, October 2017.


Received: 28 January 2017; Accepted: 21 June 2017; Published: October 2017
First available in Project Euclid: 8 September 2017

zbMATH: 1382.43013
MathSciNet: MR3708537
Digital Object Identifier: 10.1215/17358787-2017-0028

Primary: 42C99 , 43A80
Secondary: ‎43A65

Keywords: affine group , Atiyah conjecture , left translations , linear independence , Shearlet group , square-integrable representation , Weyl–Heisenberg group

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 4 • October 2017
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