向量值Nevanlinna第二基本定理的余项S(r)的估计

首先通过建立并证明推广的对数导数基本引理,讨论了１２π∫２π０ｌｏｇ＋‖ｆ′（ｒｅｉθ）‖‖ｆ（ｒｅｉθ）‖ｄθ的增长问题,进而对向量值Ｎｅｖａｎｌｉｎｎａ第二基本定理的余项进行了估计     

多尺度双向向量值小波的构造与性质

本文研究多尺度双向向量值正交小波的存在性、构造算法与性质.利用多分辨分析理论,时频分析方法与矩阵理论,给出紧支撑多尺度双向向量值正交小波的构造算法,得到多尺度双向向量值小波包的正交公式与向量值小波包基.推广了向量值正交小波的概念.     

向量值函数的Riemann-Stieltjes积分

引入向量值函数关于实值函数的Riemann-Stieltjes积分,给出了向量值Riemann-Stieltjes可积的充要条件,并讨论了积分的收敛定理.     

向量值正交小波包

引进对应于2尺度向量值尺度函数的多分辨分析和向量值小波的概念.给出向量值小波包的定义及其构造算法,研究了向量值正交小波包的正交性,并讨论了空间L2(R,CN)的正交分解.     

多尺度紧支撑向量值正交小波的构造

引入了多尺度向量值多分辨分析．利用矩阵理论,给出多尺度紧支撑向量值正交小波存在的必要条件及其构造方法．     

多重向量值正交小波包

本文引入多重向量值小波包的概念,提供一类多重向量值正交小波包的构造方法,并运用积分变换和算子理论,讨论了多重向量值正交小波包的性质．利用多重向量值正交小波包,构造了空间L2(R,Cs×s)的新的正交基．     

一类向量值正交小波的设计与性质

引入整数因子伸缩的向量值正交小波与向量值小波包的概念.运用仿酉向量滤波器理论和矩阵理论,给出具有整数因子伸缩的向量值正交小波存在的充要条件.提供了紧支撑向量值正交的构建算法,给出了相应的构建算例.利用时频分析方法与算子理论,刻画了一类向量值正交小波包的性质,得到了整数伸缩的向量值小波包的正交公式.     

复k-超正则向量值函数的性质

在实k-超正则向量值函数和实k-超调和向量值函数定义的基础上,首先给出了复k-超正则向量值函数和复k-超调和向量值函数的定义,然后引入了一个偏微分方程组,借助这个偏微分方程组讨论了复k-超正则向量值函数的性质及其与复k-超调和向量值函数的关系,最后得到这个偏微分方程组可解性的充分必要条件.     

多尺度多重向量值双正交小波的构建算法与性质

研究多尺度多重向量值双正交小波的构建算法与性质.运用向量细分格式、矩阵理论和多重向量值多分辨分析,证明了与一对给定的多尺度多重向量值双正交尺度函数对应的多尺度多重向量值双正交小波函数的存在性.提出了紧支撑多尺度多重向量值双正交小波的构造算法.讨论了多尺度多重向量值小波包的性质,得到了多重向量值小波包的双正交公式与向量值小波包基.     

向量值有理插值存在性的一种判别方法

对于向量值有理插值的计算,目前已经有多种求解算法.但其存在性的判别方法及其证明在现有的文献中还没有见到.这里利用标量有理插值函数插值存在性的思想,引入Newton基函数,给出并证明了向量值有理插值存在性的一种判别方法.同时给出有理插值函数的分子和分母的显式表达式,最后的实例说明了它的有效性.     

Some Properties of Meromorphic Solutions to Systems of Complex Differential-Difference Equations

Applying Nevanlinna theory of the value distribution of meromorphic functions, the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of complex differential-difference equations. Specifically speaking, the estimates about counting function and proximity function of meromorphic solutions to systems of complex differential-difference equations can be given.     

Estimates of N-function and m-function of meromorphic solutions of systems of complex difference equations

We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.     

Products of generalized Nevanlinna functions with symmetric rational functions

New classes of generalized Nevanlinna functions, which under multiplication with an arbitrary fixed symmetric rational function remain generalized Nevanlinna functions, are introduced. Characterizations for these classes of functions are established by connecting the canonical factorizations of the product function and the original generalized Nevanlinna function in a constructive manner. Also, a detailed functional analytic treatment of these classes of functions is carried out by investigating the connection between the realizations of the product function and the original function. The operator theoretic treatment of these realizations is based on the notions of rigged spaces, boundary triplets, and associated Weyl functions.     

An algebroid function and its derivative

In this paper, we investigate the value distribution of an algebroid function and its derivative, and obtain two inequations between Nevanlinna characteristic function of an algebroid function and that of its derivative. We extend Chuang Chitai's theorem of meromorphic functions to algebroid functions.     

The growth of algebroidal function

In this paper, we investigate the growth relationship of algebroidal function and its coefficients, and then obtain a basic inequation between the maximum modulus function and Nevanlinna characteristic function. Finally, by using the inequation, we testify the order of entire algebroidal function is equal to that of its derived function.     

代数体函数第二基本定理的一个推广

利用亚纯函数的Nevanlinna值分布理论,研究代数体函数第二基本定理的扩展形式,将该定理推广到两列互异且次数不超过d的多项式的情况,拓展了熊庆来、MillouX H等人的结果.     

The distribution of normalized zero-sets of random meromorphic functions

This paper is concerned with the distribution of normalized zero-sets of random meromorphic functions.The normalization of the zero-set plays the same role as the counting function for a meromorphic function in Nevanlinna theory.The results generalize the theory of Shiffman and Zelditch on the distribution of the zeroes of random holomorphic sections of powers of positive Hermitian holomorphic line bundles.As in a very special case,our paper resembles a form of First Main Theorem in classical Nevanlinna The...     

Extremal Problems in the Class of Delta-Subharmonic Functions of Finite Order in a Half-Plane

We obtain exact lower bounds of the upper limits of ratios of the Nevanlinna characteristics of a delta-subharmonic function in the upper half-plane.     

On locally definitizable matrix functions

We study analytic properties of special classes of matrix functions (locally definitizable and locally Nevanlinna functions) by methods of operator theory. The aim of this paper is to prove that if G(λ) is a locally definitizable or locally generalized matrix Nevanlinna function, then ?(G(λ))^?1 belongs to the same class.