ABSTRACT

In this paper, we investigate the invertibility of generalized g-Bessel multipliers. Sufficient and necessary conditions for invertibility are determined depending on the optimal g-frame bounds. Moreover, we show that, for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame multiplier with the reciprocal symbol and dual g-frames of the given ones. Furthermore, we investigate some equivalent conditions for the special case, when both dual g-frames can be chosen to be the canonical duals. Finally, we give several approaches for constructing invertible generalized g-frame multipliers from the given ones. It is worth mentioning that some of our results are quite different from those studied in the previous literatures on this topic.

摘要

在本文中，我们研究了广义 g-Bessel 乘子的可逆性。可逆性的充分和必要条件取决于最佳 g 框架边界。此外，我们表明，对于半归一化符号，任何可逆广义 g 帧乘法器的逆都可以表示为具有倒数符号和给定的对偶 g 帧的广义 g 帧乘法器。此外，我们研究了特殊情况的一些等效条件，当两个对偶 g 帧都可以选择为规范对偶时。最后，我们给出了几种从给定的构造可逆广义 g 帧乘法器的方法。值得一提的是，我们的一些结果与之前关于该主题的文献研究的结果有很大不同。