解析函数

The optimal control law obtained consists of linear analytic functions and a compensation term which is a series sum of the adjoint vectors. The analytic functions can be found by solving a Riccati matrix difference equation and a matrix difference equation. The compensation term can be obtained by a recursion formula that solves adjoint vector equations.

得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成，其解析函数由一次性求解Riccati矩阵差分方程和矩阵差分方程得到，补偿项由求解伴随向量差分方程的递推公式得到。

Analytic functions of complex variable function is the main object of study, and the five equivalent conditions of analytic functions penetrate the whole process of learning of complex function.

解析函数是复变函数论主要的研究对象，而解析函数的五个等价条件又贯穿了我们对复变函数论学习的全过程。

A comparable function can be defined in terms of the digital transfer function using the polar variable z by defining HH = HH (1/z) which gives the magnitude-squared frequency response when evaluated around the unit circle, i.e., z = ejw.

解析复杂值函数的复变S是定义在此背景下，逼近抵达中的F ，结果是一个解析函数法郎的因子F款，这是理想的过滤器传递函数在矩形的变数。

Although many results have been obtained, there are still a number of very interesting questions about composition operators unsolved. There is much more to be learned about the collective compactness and convergence of composition operator sequences, compactness of various product of composition operators, cyclicity, closed range and spectra of composition operators in various settings. Commutants of composition operators seem to be very difficult to characterize. Only a little is known about their reducing invariant subspaces. There has been no work on C〓 algebras generated by composition operators.

尽管已取得如此丰富的结果，但是关于复合算子仍然有大量非常有意义的问题值得研究，例如：复合算子序列的总体紧性及收敛性、复合算子的各种乘积的紧性、复合算子的闭值域问题、复合算子在各种解析函数空间上的谱的描述、换位复合算子的刻画、复合算子诱导的不变子空间问题、循环复合算子的研究、由复合算子生成的C〓-代数的研究、不同解析函数空间之间的加权复合算子及复合算子半群等等问题。

Iii By using the well-known properties of the dela vallee-poussin summability kernels and the pass principle of weakly compact operator, we study the weak compactness of C〓 on vector-valued analytic function spaces H〓, B〓, N and N〓, establish some connections between the weak compactness of composition operators and the structure properties of Banach spaces. These generalize and unify the corresponding results in the scalar-valued setting and enrich the content of the study of composition operator in another way.

第三，利用著名的de la Vallee-poussin可和核及有关算子的弱紧性的传递原理给出了向量值解析函数空间H〓、B〓、N及N〓上的复合算子的弱紧性的刻画，建立了复合算子的弱紧性与Banach空间的结构性质之间的联系，统一和推广了对应的数量值解析函数空间上的复合算子的弱紧性，这从另一种途径极大地丰富了复合算子的研究内容。

We establish some connections between geometric properties, properties in analysis and analytic properties of the inducing map ψ and operatortheoretic properties of composition operator C〓: f〓fοψ on various analytic function spaces mentioned above, include the boundedness, compactness, weak compactness, collective compactness and the Schatten class operator ideal, etc. Our results extend some previous results, for instance, the Shapiro's Nevanlinna counting function condition and the MacCluer's Carleson measure condition for the compactness of C〓 on Hardy space.

本文建立了D上解析自映射φ：D→D的几何性质、分析性质和解析性质与复合算子C〓：f→foφ在上述各种解析函数空间上的限制的算子性质之间的联系，涉及到复合算子C〓的有界性、紧性、弱紧性、总体紧性及Schatten类算子理想等算子特征，推广了前人的一系列结果，如Shapiro关于C〓的紧性的Nevanlinna计数函数条件，MacCluer关于C〓的紧性的Carleson测度条件等。

Starting from the concept of conjugate analytic function,this paper expounds on the necessary and sufficient conditions of conjugate analytic of differentiable complex function represented in exponent form.

在共轭解析函数定义基础上，讨论指数形式表示的函数共轭解析的充要条件

This article uses the implicit function theorem and the properties of analytic functions,with less limitations for the uniqueness,continuity,continuous differentiability of the implicit functions,and gets the sufficient and necessary conditions of the existence of implicit functions by simplifying them.

从常用隐函数存在性定理出发，放宽对隐函数唯一、连续、连续可微等性质的限制，利用解析函数的性质将其展拓，得到广义隐函数存在的充分必要条件和广义隐函数的分布特征。

By using them, we can discuss the theory of holomorphic functions on domains: the characterization of zeros sets of holomorphic functions on the boundary, the characterization of A infinity interpolation sets on the boundary, etc.

对于复椭球和广义复椭球，我们给出了其全纯支撑函数的估计，构造了边界上的拟距离，并用这些结果来研究域上的解析函数论：边界上解析函数零点集的刻划，A无穷插值集的刻划等。

The research of bianalytic functions, polyanalytic functions and inverse Riemann boundary value problems is an important question for discussion in recently years.

近年来有关双解析函数、多解析函数以及Riemann边值逆问题的理论研究也是人们关注的重要课题。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失