动态采样：混合标架算子、表示和扰动
Dynamical sampling: mixed frame operators, representations and perturbations
摘要：
基于框架的算子表示的最新进展，我们研究了$ I=\mathbb{N}, \mathbb{Z} $的$ \{T^n φ\}_{n\in I}$形式的框架，并回答了关于有界线性算子的幂的作用引起的表示、扰动和框架的问题.作为一个特殊的情况下，我们讨论的问题表示的框架的混合框架运营商的迭代。作为我们的另一个贡献，我们考虑了非零标量$ \{a_n\}_{n=0}^{\infty} $的形式为$ \{a_n T^n φ\}_{n=0}^{\infty} $的标架，并在动态采样中得到了一些新的结果。最后，我们将提出一些辅助结果有关的扰动序列的形式$ \{T^n φ\}_{n=0}^{\infty}$。
英文摘要：
Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n φ\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames induced by the action of powers of bounded linear operators. As a particular case, we discuss problems concerning representation of frames in terms of iterations of the mixed frame operators. As our another contribution, we consider frames of the form $ \{a_n T^n φ\}_{n=0}^{\infty} $ for some non-zero scalars $ \{a_n\}_{n=0}^{\infty} $, and we obtain some new results in dynamical sampling. Finally, we will present some auxiliary results related to the perturbation of sequences of the form $ \{T^n φ\}_{n=0}^{\infty}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
