Glasnik matematički, Vol. 50 No. 1, 2015.
Original scientific paper
https://doi.org/10.3336/gm.50.1.11
On quasi-greedy bases associated with unitary representations of countable groups
Morten Nielsen
orcid.org/0000-0002-9078-0594
; Department of Mathematical Sciences, Aalborg University , DK-9220 Aalborg, Denmark
Abstract
We consider the natural generating system for a cyclic subspace of a Hilbert space generated by a dual integrable unitary representation of a countable abelian group. We prove, under mild hypothesis, that whenever the generating system is a quasi-greedy basis it must also be an unconditional Riesz basis. A number of applications to Gabor systems and to general Vilenkin systems are considered. In particular, we show that any Gabor Schauder basis that also forms a quasi-greedy system in L2 is in fact a Riesz basis, and therefore satisfies the classical Balian-Low theorem.
Keywords
Quasi-greedy bases; dual integrable representation; Gabor systems; integer translates; Vilenkin system
Hrčak ID:
140094
URI
Publication date:
15.6.2015.
Visits: 1.084 *