Wiener汞齐空间上Gabor框架算子的可逆性
Invertibility of the Gabor frame operator on the Wiener amalgam space
摘要：
我们利用Wiener的$1/f$定理的推广证明了：对于生成元在Wiener汞齐空间$W(L^{\infty}, \ell^{1}_ν)(\mathbb{R}^{d})$中的Gabor框架，相应的框架算子在该空间上是可逆的.因此，对于这样的Gabor框架，规范对偶的生成元也属于$W(L^{\infty}, \ell^{1}_ν)(\mathbb{R}^{d}) $
英文摘要：
We use a generalization of Wiener's $1/f$ theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space $W(L^{\infty}, \ell^{1}_ν)(\mathbb{R}^{d})$, the corresponding frame operator is invertible on this space. Therefore, for such a Gabor frame, the generator of the canonical dual belongs also to $W(L^{\infty}, \ell^{1}_ν)(\mathbb{R}^{d}) $
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