Three Problems on Exponential Bases

Carli, Laura De ; Mizrahi, Alberto ; Tepper, Alexander

Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 55-70

Résumé

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 $L^{2}(D)$.

Détail

DOI : 10.4153/CMB-2018-015-6

Mots-clés : exponential basis, frame, Riesz sequence, lattice

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