AI 中文总结
研究引入块对角卡尔森框架，在生成算子为特定若尔当块直和时对其分类，指出其有高冗余特性，且在生成算子非负谱、自然密度存在时给出框架冗余性完整描述。
AI 中文摘要
我们引入了“块对角卡尔森框架”，即生成算子为块对角的单生成动力框架。当生成算子是大小一致有界的若尔当块的直和时，我们对所有此类框架进行了分类。此外，块对角卡尔森框架具有卡尔森框架所具有的高冗余特性。当生成算子具有非负谱时，在自然密度存在的假设下，我们给出了此类框架冗余性的完整描述。
英文摘要
We introduce \textit{block diagonal Carleson frames}, i.e. singly generated dynamical frames in which the generating operator is block diagonal. We classify all such frames when the generating operator is a direct sum of Jordan blocks, the sizes of which are uniformly bounded. Furthermore, block diagonal Carleson frames are shown to enjoy the high redundancy properties observed for Carleson frames. When the generating operator has nonnegative spectrum, we provide a complete description of the redundancy of such frames under the assumption of the existence of natural density.
