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Three Problems on Exponential Bases

  • Laura De Carli (a1), Alberto Mizrahi (a1) and Alexander Tepper (a1)
Abstract

We consider three special and significant cases of the following problem. Let $D\subset \mathbb{R}^{d}$ be a (possibly unbounded) set of finite Lebesgue measure. Let $E(\mathbb{Z}^{d})=\{e^{2\unicode[STIX]{x1D70B}ix\cdot n}\}\text{}_{n\in \mathbb{Z}^{d}}$ be the standard exponential basis on the unit cube of $\mathbb{R}^{d}$ . Find conditions on $D$ for which $E(\mathbb{Z}^{d})$ is a frame, a Riesz sequence, or a Riesz basis for $L^{2}(D)$ .

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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