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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

Sažetak

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.

Ključne riječi

Quasi-greedy bases; dual integrable representation; Gabor systems; integer translates; Vilenkin system

Hrčak ID:

140094

URI

https://hrcak.srce.hr/140094

Datum izdavanja:

15.6.2015.

Posjeta: 1.054 *