Geodesic
Three Problems on Exponential Bases
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 55-70

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DOI

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 $L^{2}(D)$.
DOI : 10.4153/CMB-2018-015-6
Mots-clés : exponential basis, frame, Riesz sequence, lattice 
Carli, Laura De; Mizrahi, Alberto; Tepper, Alexander. Three Problems on Exponential Bases. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 55-70. doi: 10.4153/CMB-2018-015-6
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     title = {Three {Problems} on {Exponential} {Bases}},
     journal = {Canadian mathematical bulletin},
     pages = {55--70},
     year = {2019},
     volume = {62},
     number = {1},
     doi = {10.4153/CMB-2018-015-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-015-6/}
}
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