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Discrete and Continuous Balian-Low Theorems in Several Dimensions. (arXiv:1807.03856v1 [math.CA])
来源于:arXiv
Recently, Shahaf Nitzan and Jan-Fredrik Olsen showed that Balian-Low type
theorems exist for discrete Gabor systems defined on $\mathbb{Z}_d$. Here, we
extend these results to higher dimensional analogs of these systems on
$\mathbb{Z}_d^{l}$, and show a variety of applications of both the discrete and
continuous verisons of the so-called Quantitative Balian-Low Theorem, also of
Nitzan and Olsen. In particular, we prove nonsymmetric versions of the finite
and continuous Balian-Low Theorems holding for $\ell_2(\mathbb{Z}_d^l)$ and
$L^2(\mathbb{R}^l)$, respectively. 查看全文>>