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Duals of Weighted Exponential Systems

Duals of Weighted Exponential Systems The paper considers the basis and frame properties of the system of weighted exponentials ${\mathcal{E}}(g,\mathbb{Z}\backslash F) = \{e^{2\pi i n x} g(x)\}_{n\in\mathbb{Z}\backslash F}$ in $L^{2}({\mathbb{T}})$ , where $g \in L^{2}({\mathbb{T}}) \backslash\{0\}$ and F⊂ℤ. It is shown that many of the frame properties of ${\mathcal {E}}(g,\mathbb{Z}\backslash F)$ are affected by the cardinalities of F and the behavior of the zeros of g. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Duals of Weighted Exponential Systems

Acta Applicandae Mathematicae , Volume 119 (1) – Dec 16, 2011

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media B.V.
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity; Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-011-9663-1
Publisher site
See Article on Publisher Site

Abstract

The paper considers the basis and frame properties of the system of weighted exponentials ${\mathcal{E}}(g,\mathbb{Z}\backslash F) = \{e^{2\pi i n x} g(x)\}_{n\in\mathbb{Z}\backslash F}$ in $L^{2}({\mathbb{T}})$ , where $g \in L^{2}({\mathbb{T}}) \backslash\{0\}$ and F⊂ℤ. It is shown that many of the frame properties of ${\mathcal {E}}(g,\mathbb{Z}\backslash F)$ are affected by the cardinalities of F and the behavior of the zeros of g.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 16, 2011

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