共查询到20条相似文献,搜索用时 31 毫秒
1.
研究了单位圆内代数体函数涉及重值的Borel点的存在性,利用型函数统一证明了单位圆内无穷级,有限正级和部分零级代数体函数存在涉及重值的Borel点,并对有限正级的代数体函数得到两个必要条件. 相似文献
2.
该文证明了平面上满足一定条件的零级代数体函数至少存在一条强Borel方向,并且它还是通常的关于型函数的Borel方向. 相似文献
3.
覆盖曲面定理与代数体函数的重值 总被引:9,自引:0,他引:9
本文改进了Tsuji著名的球面有限连通覆盖定理,应用它建立了关于涉及代数体函数重值的基本不等式,并由此导出了有限正级代数体函数涉及其重值的充满圆序列及Borel方向的精确结果. 相似文献
4.
In this article several theorems of the theory of Γ-lines for meromorphic functions are extended to the more general setting
of algebroid functions. We recall the definition of algebroid function of order k and how it can be considered as a function defined on a Riemann surface of k sheets. In this way, we prove the so called tangent variation principle for algebroid functions, previously proved for meromorphic
functions by Barsegian, and we get several consequences of this result. We also extend a proposition on proximity properties
of meromorphic functions. 相似文献
5.
In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations are closed. On basis of these works, we firstly prove the Second Main Theorem concerning small algebroid functions for v-valued algebroid functions. 相似文献
6.
In this paper, we discuss the influence of multiple values and Valiron deficiencies on the uniqueness problem of algebroid functions on annuli, we get the several uniqueness theorems of algebroid functions on annuli, and also we extend the Nevanlinna value distribution theory for algebroid functions on annuli. 相似文献
7.
First we prove a new inequality comparing uniformly the relative volume of a Borel subset with respect to any given complex
euclidean ballB⊂C
n
with its relative logarithmic capacity inC
n
with respect to the same ballB. An analogous comparison inequality for Borel subsets of euclidean balls of any generic real subspace ofC
n
is also proved.
Then we give several interesting applications of these inequalities. First we obtain sharp uniform estimates on the relative
size of plurisubharmonic lemniscates associated to the Lelong class of plurisubharmonic functions of logarithmic singularities
at infinity onC
n
as well as the Cegrell class of plurisubharmonic functions of bounded Monge-Ampère mass on a hyperconvex domain Ω⊂(C
n
.
Then we also deduce new results on the global behaviour of both the Lelong class and the Cegrell class of plurisubharmonic
functions.
This work was partially supported by the programmes PARS MI 07 and AI.MA 180. 相似文献
8.
In this paper,we define the shared value of an algebroid function and its derivative on its Riemann surface.By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives,we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives,which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen. 相似文献
9.
《数学物理学报(B辑英文版)》2015,(3)
Guided by Lo.Yang's method,we concern the question that how algebroid functions are determined by their multiple values and deficient values and we prove an at most3v-valued theorem for algebroid functions.The results are complemented by an example for completeness. 相似文献
10.
代数体亚纯函数的最大型Borel方向 总被引:5,自引:1,他引:4
本文参考李国平的半纯函数聚值线的统一理论,证明了当r→∞时,T(r,W)/log^2r的上极限等于∞的有限级(包含零级)的代数亚纯函数的最大型Borel方向的存在性,所得结果推广了本国平在亚纯函数中的结果。 相似文献
11.
In this article, by comparing the characteristic functions, we prove that for any ν-valued algebroid function w(z) defined in the open unit disk with ${\limsup_{r\rightarrow1-}T(r,w)/\log\frac{1}{1-r}=\infty}$ and the hyper order ρ 2(w)?=?0, the distribution of the Borel radii of w(z) and w′(z) is the same. This is the extension of G. Valiron’s conjecture for the meromorphic functions defined in ${\widehat{\mathbb{C}}}$ . 相似文献
12.
张庆彩 《数学的实践与认识》2013,43(1)
研究涉及导函数的代数体函数的唯一性.证明了设w(z)为开复平面内不可约的v值代数体函数,a_i(i=1,2,…,4v-1)为判别的有穷复数,如果w(z)与w'(z)以a_1,a_2,…,a_(4v-1),∞为IM公共值,则w(z)≡w'(z). 相似文献
13.
14.
研究了代数体函数w(z)的Borel方向和确定该代数体函数的复方程A_k(z)w~k+_(Ak-1)(z)w~_(k-1)+…+A_0(z)=0的系数函数A_k(z),A_(k-1)(z),…,A_0(z)的Borel方向之间的关系. 相似文献
15.
《数学物理学报(B辑英文版)》2020,(4)
In this article, we discuss, by Nevanlinna theory, the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions. We get several uniqueness theorems of algebroid functions which include an at most 3 v-valued theorem. These results extend the existing achievements of some scholars. 相似文献
16.
《数学物理学报(B辑英文版)》2016,(1)
In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we generalized a theorem of Li Guoping's. 相似文献
17.
18.
应用Ahlfors覆盖曲面的几何方法,证明了单位圆内无限级代数体函数的Borel点的存在性.将Valiron关于无限级Borel方向存在性的结果推广到了单位圆内. 相似文献
19.
Zu-Xing Xuan 《Journal of Mathematical Analysis and Applications》2008,341(1):540-547
In this paper, we solve a problem of J.H. Zheng (see Problem 5.12 of [J.H. Zheng, On value distribution of meromorphic functions with respect to arguments, preprint]) by proving that for any ν-valued algebroid function satisfying , there exists a T-direction dealing with multiple values of w(z). 相似文献
20.
LetI be a σ-ideal on a Polish space such that each set fromI is contained in a Borel set fromI. We say thatI fails to fulfil theΣ
1
1
countable chain condition if there is aΣ
1
1
equivalence relation with uncountably many equivalence classes none of which is inI. Assuming definable determinacy, we show that if the family of Borel sets fromI is definable in the codes of Borel sets, then eachΣ
1
1
set is equal to a Borel set modulo a set fromI iffI fulfils theΣ
1
1
countable chain condition. Further we characterize the σ-idealsI generated by closed sets that satisfy the countable chain condition or, equivalently in this case, the approximation property
forΣ
1
1
sets mentioned above. It turns out that they are exactly of the formMGR(F)={A : ∀F ∈ F
A ∩F is meager inF} for a countable family F of closed sets. In particular, we verify partially a conjecture of Kunen by showing that the σ-ideal of meager sets is the
unique σ-ideal onR, or any Polish group, generated by closed sets which is invariant under translations and satisfies the countable chain condition.
Research partially supported by NSF grant DMS-9317509. 相似文献