有限迭代级整系数线性微分方程解的性质

研究了有限迭代级整系数的复线性微分方程,应用Nevalinna和Ahlfors的角域理论,得到了有关解的迭代级,零点迭代收敛指数以及角域中的零点分布的结果．     

Characteristic of composite functions of entire function with saturated defective number

In this article we solved some problems due to Yang concerning the characteristic function of the composite functions.     

Uniqueness of entire functions

Let f be a nonconstant entire function and let a be a meromorphic function satisfying T(r,a)=S(r,f) and a?a′. If f(z)=a(z)⇔f′(z)=a(z) and f(z)=a(z)⇒f″(z)=a(z), then f≡f′, and a?a′ is necessary. This extended a result due to Jank, Mues and Volkmann.     

关于整函数超级的进一步结果

运用正规族理论研究了整函数与其高阶导数分担无穷级函数增长级与超级的相关结果.从亚纯函数超级大于零而使球面导数无界的角度出发,然后综合运用Pang-Zaclman引理,数学归纳法和Nevanlinna理论等方法证明了该结果,推广和改进了已有的结果.     

一类二阶线性微分方程解的增长性

本文研究一类二阶齐次线性微分方程f"+A_1(z)e~(P(z))f'+A_0(z)e~(Q(z))f=0,解的增长性,其中P(z)=az~n,Q(z)=bz~n,ab≠0,a=cb(c1),A_j(z)(j=0,1)是非零多项式,证明了该方程的每个非零解满足σ(f)=∞并且σ_2(f)=n.     

ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS＊＊

The author investigates the hyper order of Solutions of the higher order linear equation, and improves the results of M. Ozawa[15], G. Gundersen[6] and J. K. Langley[12].     

Uniqueness and value-sharing of entire functions

In this paper, we study the uniqueness problems on entire functions sharing one value with the same multiplicities. We generalize and unify some previous results of Fang and Hua [M.L. Fang, X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly 13 (1) (1996) 44-48], Yang and Hua [C.C. Yang, X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (2) (1997) 395-406] and Fang [M.L. Fang, Uniqueness and value-sharing of entire functions, Comput. Math. Appl. 44 (2002) 828-831].     

关于高阶整函数系数微分方程解的增长性

研究了两类高阶线性整函数系数微分方程解的增长性，得到了其超级的精确估计，文中的定理改进了G.Gundersen和陈宗煊的有关结果。     

On sums of roots of infinite order entire functions

A class of infinite order entire functions is considered. Estimates for sums of the roots are derived. These estimates supplement the Hadamard theorem. Moreover, we establish a new estimate for the counting function of the roots, which in appropriate situations can be more useful than the Jensen inequality.     

Strongly regular growth of entire functions of order zero

For entire functions of order zero we introduce a new concept of regularity of growth, which is shown to possess properties similar to those which characterize the concept of totally regular growth of entire functions of finite order in the sense of Levin-Pflüger. Translated fromMatematicheskie Zameiki, Vol. 63, No. 2, pp. 196–208, February, 1998. This research was partially supported by the International Science Foundation under grant No. UCR000.     

On a non-standard class of entire functions

In this article we construct a class of entire functions of arbitrary finite order and with non-zero Taylor coefficients, which is not written in the form of Hadamard's canonical product. Some basic properties of this class are also given.     

Entire functions that share a small function with their derivatives

Let f be an entire function of finite order and a an entire function of order less than f's. If f−a and f^′−a have the same zeros with the same multiplicities, then f^′−a≡c(f−a) for some non-zero constant c.     

关于高阶整函数系数微分方程解的增长性的进一步结果

本文研究一类高阶整函数系数微分方程的增长性问题，当存在某个系数对方程的解的性质起主要支配作用时，得到了齐次与非齐次方程解的超级的精确估计及方程的解与小函数的关系。     

Entire functions sharing an entire function of smaller order with their difference operators

We study a uniqueness question of entire functions order with their difference operators, and deal with a question in this paper extend the corresponding results obtained by Liu Examples are provided to show that the results in this paper, in sharing an entire function of smaller posed by Liu and Yang. The results -Yang and by Liu-Laine respectively. a sense, are the best possible.     

Approximation numbers for composition operators on spaces of entire functions

We study the degree of compactness of composition operators $C_{\phi }$ acting on weighted Hilbert spaces of entire functions, which include (i) the space of entire Dirichlet series, (ii) the space of entire power series, and (iii) the Fock space (we must have $\phi \left(z\right)=az+b$, and it is known that $C_{\phi }$ is compact if and only if $\left|a\right|<1$). More precisely, the sequence $\left(a_n\right)$ of approximation numbers of $C_{\phi }$ is investigated: for (i), we give the exact formula for $\left(a_n\right)$, while for (ii) and (iii) we give upper and lower estimates for $a_n$, showing that $a_n$ behaves like ${\left|a\right|}^n$ up to a subexponential factor. In particular, $C_{\phi }$ belongs to all Schatten classes $S_p,p>0$ as soon as it is compact.     

Entire solutions of differential equations with finite order transcendental entire coefficients

In this paper, we investigate the complex oscillation of the differential equation

Normal families and uniqueness theorems for entire functions

There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S,f)=E(S,f′), then f≡f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.     

On meromorphic functions with finite logarithmic order

By using a slow growth scale, the logarithmic order, with which to measure the growth of functions, we obtain basic results on the value distribution of a class of meromorphic functions of zero order.

     

Complete systems of partial derivatives of entire functions and frequently hypercyclic operators

We find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space H(C^d)$H({\mathbb{C}}^d)$ of all entire functions of d   variables. As an application of this result we describe new classes of frequently hypercyclic operators on H(C^d)$H({\mathbb{C}}^d)$.