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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Riesz bases of exponentials on multiband spectra


Author: Nir Lev
Journal: Proc. Amer. Math. Soc. 140 (2012), 3127-3132
MSC (2010): Primary 42C15, 94A12
Published electronically: January 18, 2012
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Abstract: Let $ S$ be the union of finitely many disjoint intervals on $ \mathbb{R}$. Suppose that there are two real numbers $ \alpha , \beta $ such that the length of each interval belongs to $ \mathbb{Z} \alpha + \mathbb{Z}\beta $. We use quasicrystals to construct a discrete set $ \Lambda \subset \mathbb{R}$ such that the system of exponentials $ \{\exp 2 \pi i \lambda x, \, \lambda \in \Lambda \}$ is a Riesz basis in the space $ L^2(S)$.


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Additional Information

Nir Lev
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Email: nir.lev@weizmann.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11138-4
PII: S 0002-9939(2012)11138-4
Keywords: Riesz bases, multiband signals, quasicrystals
Received by editor(s): February 6, 2011
Received by editor(s) in revised form: March 21, 2011
Published electronically: January 18, 2012
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.