We characterize the normal operators A on \(\ell ^2\) and the elements \(a^i \in \ell ^2\), with \(1\le i\le m\), such that the sequence

$$\begin{aligned} \{ A^n a^1, \ldots , A^n a^m \}_{n\ge 0} \end{aligned}$$

is a frame. The characterization makes strong use of the pseudo-hyperbolic metric of \( {{\mathbb {D}}} \) and is given in terms of the backward shift invariant subspaces of \(H^2( {{\mathbb {D}}} )\) associated to finite products of interpolating Blaschke products.

中文翻译：

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通过模型空间的多轨道框架

我们用\（1 \ le i \ le m \）刻画\（\ ell ^ 2 \）上的普通算子A和元素\（a ^ i \ in \ ell ^ 2 \）的特征，使得序列

$$ \ begin {aligned} \ {A ^ na ^ 1，\ ldots，A ^ na ^ m \} _ {n \ ge 0} \ end {aligned} $$

是一个框架。表征充分利用了\（{{{mathbb {D}}} \）的伪双曲度量，并根据\（H ^ 2（{{\ mathbb {D} }}）\）与内插Blaschke积的有限积相关。