Riesz bases of exponentials on multiband spectra
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- by Nir Lev PDF
- Proc. Amer. Math. Soc. 140 (2012), 3127-3132 Request permission
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
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Additional Information
- Nir Lev
- Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
- MR Author ID: 760715
- Email: nir.lev@weizmann.ac.il
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3127-3132
- MSC (2010): Primary 42C15, 94A12
- DOI: https://doi.org/10.1090/S0002-9939-2012-11138-4
- MathSciNet review: 2917085