AI 中文总结
该研究推广了Nevanlinna-Pick插值理论，建立了相关算子理论框架，证明了H^∞(𝔻)成员关系的普遍检测方法，并揭示非交换内簇上Arveson型完全谱集表示失效的特性。
AI 中文摘要
我们建立了有限Blaschke乘积f作用下不变函数的Nevanlinna-Pick插值的动态推广，将轨道空间上的全局有界全纯延拓问题归结为结构化块核正性问题。此外，我们证明，通过任意有限Blaschke乘积的变形可普遍检测H^∞(𝔻)的成员关系。这些结果是通过遵循Sarason思想的协变算子对的基础算子理论提升框架证明的。最后，在非交换函数理论背景下，我们表明，尽管矩阵值von Neumann不等式在自由多圆盘上普遍成立，但Arveson型完全谱集表示在非交换内簇上失效。
英文摘要
We establish a dynamic generalization of Nevanlinna-Pick interpolation for functions invariant under the action of a finite Blaschke product $f$, reducing global bounded holomorphic extension on orbit spaces to structured block-kernel positivity. Furthermore, we demonstrate that membership in $H^\infty(\mathbb{D})$ is universally detectable via deformations by any finite Blaschke product. These results are proved via an underlying operator-theoretic lifting framework for covariant operator pairs in the spirit of Sarason. Finally, in the setting of non-commutative function theory, we show that despite the universal validity of the matrix-valued von Neumann inequality over the free polydisk, Arveson-type complete spectral set representations break down for non-commutative inner varieties.
Comments24 pages; Comments welcome
