Matrix-J-unitary Non-commutative Rational Formal Power Series
Matrix-J-unitary Non-commutative Rational Formal Power Series
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矩阵-J-酉非交换有理式幂级数
DOI：
10.1007/3-7643-7431-4_2
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
D. S. Kalyuzhnyı̆
中科院分区：
文献类型：
--
作者：
Daniel Alpay;D. S. Kalyuzhnyı̆
N个非对易不定元的形式幂级数可以看作是在0处全纯的一元函数的对应物，并且用系数描述了它们的一些性质。然而，真正富有成效的分析开始于考虑对n × n矩阵（n = 1，2，…）的N元组或无限维可分希尔伯特空间上的算子的求值。此外，这种评估出现在现代系统工程的控制，优化和稳定问题。
Formal power series in N non-commuting indeterminates can be considered as a counterpart of functions of one variable holomorphic at 0, and some of their properties are described in terms of coefficients. However, really fruitful analysis begins when one considers for them evaluations on N-tuples of n × n matrices (with n = 1, 2, ⋯) or operators on an infinite-dimensional separable Hilbert space. Moreover, such evaluations appear in control, optimization and stabilization problems of modern system engineering.