与$μ$合成相关的结构域家族
A family of domains associated with $μ$-synthesis
摘要：
我们介绍一个家族的结构域-我们称之为$μ_{1,n}$ -与$μ$ -合成的一个方面有关。我们表明，自然协会的对称化polydisc具有相应的光谱单位球也表现出的$μ_{1,n}$商和它的相关单位“$μ_E$球”。这里，$μ_E$是情况$E = \{[w]\oplus(z I_{n-1})\in \mathbb{C}^{n\times n}: z,w\in \mathbb{C}\}$的结构化奇异值，n = 2，3，4，.具体而言：我们证明了，对于这样的$E$，具有单位“$μ_E$ -球”中的矩阵数据的Nevanlinna-Pick插值问题，以及在精确意义上的一般位置，等价于对于相关的$μ_{1,n}$ -商的Nevanlinna-Pick插值问题。在此过程中，我们给出了$μ_{1,n}$ -子的一些特征。
英文摘要：
We introduce a family of domains --- which we call the $μ_{1,n}$-quotients --- associated with an aspect of $μ$-synthesis. We show that the natural association that the symmetrized polydisc has with the corresponding spectral unit ball is also exhibited by the $μ_{1,n}$-quotient and its associated unit "$μ_E$-ball". Here, $μ_E$ is the structured singular value for the case $E = \{[w]\oplus(z I_{n-1})\in \mathbb{C}^{n\times n}: z,w\in \mathbb{C}\}$, n = 2, 3, 4,... Specifically: we show that, for such an $E$, the Nevanlinna-Pick interpolation problem with matricial data in a unit "$μ_E$-ball", and in general position in a precise sense, is equivalent to a Nevanlinna-Pick interpolation problem for the associated $μ_{1,n}$-quotient. Along the way, we present some characterizations for the $μ_{1,n}$-quotients.
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