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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
MathSciNet review: 2917085
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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)$.

References [Enhancements On Off] (What's this?)

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Additional Information

Nir Lev
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel

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.

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