论文标题
部分可观测时空混沌系统的无模型预测
The Cowen-Douglas Theory for Operator Tuples and Similarity
论文作者
论文摘要
我们关注Cowen-Douglas操作员的相似性问题。 1970年代已经研究了统一的等效性，以及包括向量束和曲率在内的几何概念出现在描述中。正如Cowen-Douglas的猜想所表明的那样，直到最近，对相似性问题的研究一直还没有成功。最新结果揭示了复杂的几何形状，电晕问题和单个库芬 - 道格拉斯操作员的相似性问题之间的密切相关性。如果不利用不再在多变量设置中持有的电晕定理，我们证明了单一操作员的相似性结果对于通勤Cowen-Douglas Operator clutter buts butsialition。
We are concerned with the similarity problem for Cowen-Douglas operator tuples. The unitary equivalence counterpart was already investigated in the 1970's and geometric concepts including vector bundles and curvature appeared in the description. As the Cowen-Douglas conjecture show, the study of the similarity problem has not been so successful until quite recently. The latest results reveal the close correlation between complex geometry, the corona problem, and the similarity problem for single Cowen-Douglas operators. Without making use of the corona theorems that no longer hold in the multi-variable setting, we prove that the single operator results for similarity remain true for commuting Cowen-Douglas operator tuples as well.
