共查询到20条相似文献,搜索用时 31 毫秒
1.
We characterise interpolating and sampling sequences for the spaces
of entire functions f such that $ f e^{-\phi}\in L^p(\C)$, $p\geq 1 $, where $\phi$ is
a subharmonic weight whose Laplacian is a doubling measure. The
results are expressed in terms of some densities adapted to the metric
induced by $\Delta\phi$. They generalise previous results by Seip for the case
$\phi(z)=|z|^2$, Berndtsson and Ortega-Cerdà and Ortega-Cerdà and Seip
for the case when $\Delta\phi$ is bounded above and below, and Lyubarskiĭ
and Seip for 1-homogeneous weights of the form $\phi(z)=|z|h(\arg z)$,
where h is a trigonometrically strictly convex function. 相似文献
2.
Fixed points of meromorphic functions and of their differences,divided differences and shifts
下载免费PDF全文
![点击此处可从《数学学报(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Let f(z) be a finite order meromorphic function and let c∈C\{0} be a constant.If f(z)has a Borel exceptional value a∈C,it is proved that max{τ(f(z)),τ(△_cf(z))}=max{τ(f(z)),τ(f(z+c))}=max{τ(△_cf(z)),τ(f(z+c))}=σ(f(z)).If f(z) has a Borel exceptional value b∈(C\{0})∪{∞},it is proved that max{τ(f(z)),τ(△cf(z)/f(z))}=max{τ(△cf(z)/f(z)),τ(f(z+c))}=σ(f(z)) unless f(z) takes a special form.Here τ(g(z)) denotes the exponent of convergence of fixed points of the meromorphic function g(z),and σ(g(z)) denotes the order of growth of g(z). 相似文献
3.
设k,n(≥k+1)是两个正整数,a(≠0),b是两个有穷复数,F为区域D内的一族亚纯函数.如果对于任意的f∈F,f的零点重级大于等于k+1,并且在D内满足f+a[L(f)]~n-b至多有n-k-1个判别的零点,那么F在D内正规·这里L(f)=f~((k))(z)+a_1f~((k-1))(z)+…+a_(k-1)f'(z)+a_kf(z),其中a_1(z),a_2(z),…,a_k(z)是区域D上的全纯函数. 相似文献
4.
本文首先引入满足如下条件$$-\frac{qzD_{q}f(z)}{f(z)}\prec \varphi (z)$$和$$\frac{-(1-\frac{\alpha }{q})qzD_{q}f(z)+\alpha qzD_{q}[zD_{q}f(z)]}{(1-\frac{\alpha}{q})f(z)-\alpha zD_{q}f(z)}\prec \varphi (z)~(\alpha \in\mathbb{C}\backslash (0,1],\ 0
相似文献
5.
Wojciech Szapiel 《Journal d'Analyse Mathématique》2010,111(1):47-76
Denote by B(τ) the class of all complex functions of the form
$
f(z) \equiv \tau + \sum\limits_{n = 1}^\infty {(a_n (f)z^n + \overline {b_n (f)} \bar z^n )}
$
f(z) \equiv \tau + \sum\limits_{n = 1}^\infty {(a_n (f)z^n + \overline {b_n (f)} \bar z^n )}
相似文献
6.
Arturo Fernández Arias 《Complex Analysis and Operator Theory》2017,11(8):1653-1668
The study of meromorphic functions without multiple values in the plane started by F. Nevanlinna is extended to meromorphic functions in the punctured plane \({\mathbb {C}}^{{*}}.\) It is a classical result that a meromorphic function \(f\left( z\right) \) can be obtained as quotient of solutions of the second order differential equation \(u^{{\prime \prime }}+\left\{ f\left( z\right) ,z\right\} u=0,\) where \(\left\{ f\left( z\right) ,z\right\} \) is the Schwarzian derivative of \(f\left( z\right) \). In our hypothesis of meromorphic functions of finite order without multiple values in the puntured plane, the Schwarzian derivative \(\left\{ f\left( z\right) , z\right\} \) turns out to be a rational function with only possible poles at 0 and \(\infty \). In these conditions the asymptotic behaviour of \(f\left( z\right) \) can be described by a result of Hille (Lectures on Ordinary Differential Equations in the complex plane, Addison Wesley, Boston, 1969) on ordinary differential equations in the complex plane. The results obtained are framed in the value distribution theory of meromorphic functions, in particular in the punctured plane we shall consider the work of Khrystiyanin and Kondratyuk (Mat Stud 23(1):19–30, 2005; Mat Stud 23(1):57–68, 2005) and Korhonen (Nevanlinna theory on an annulus. Value distribution theory and related topics. Adv. Complex analysis and applications, Kluwer Academic Publishers, Dordrecht, 2004). 相似文献
7.
Let $I$ be an open interval of $\mathbb{R}$ and $f: I\to \mathbb{R}$. It is well-known that $f$ is convex in $I$ if and only if, for all $x,y\in I$ with $x
8.
Letf∈A ρ (ρ>1), whereA ρ denotes the class of functions analytic in ¦z¦ <ρ but not in ¦z¦≤ρ. For any positive integerl, the quantity Δ l,n?1(f; z) (see (2.3)) has been studied extensively. Recently, V. Totik has obtained some quantitative estimates for \(\overline {\lim _{n \to \infty } } \max _{\left| z \right| = R} \left| {\Delta _{l,n - 1}^ - \left( {f;z} \right)} \right|^{1/n} \) . Here we investigate the order of pointwise convergence (or divergence) of Δ l,n?1(f; z), i.e., we study \(B_1 \left( {f;z} \right) = \overline {\lim _{n \to \infty } } \left| {\Delta _{l,n - 1} \left( {f;z} \right)} \right|^{1/n} \) . We also study some problems arising from the results of Totik. 相似文献
9.
设F是区域D上的一个亚纯函数族,k(≥2)是一个正整数,b是一个非零复数,M是一个正数.若对任意给定的f∈F,f的零点重数至少为k,且f(z)=0=|f~((k))(z)|≤M.如果对任意给定的函数f,g∈F,L(f)与L(g)的零点都为重零点,且L(f)与L(g)在区域D内分担b,则F在区域D内正规. 相似文献
10.
设F是平面区域D上的亚纯函数族,a,b是两个有穷非零复数.如果■ff∈F,f(z)=a■f~((k))(z)=a,ff~((k))(z)=b■f~((k+1))(z)=b,且f-a的零点重数至少为k(k≥3),那么函数族F在D内正规;当k=2时,在条件a≠4b的情况下,同样有函数族F在D内正规. 相似文献
11.
In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental entire function with ρ(A)<1/2.Suppose that k≥2 and f(k)+A(z)f=0 has a solution f with λ(f)<ρ(A),and suppose that A1=A+h,where h≡0 is an entire function with ρ(h)<ρ(A).Then g(k)+A1(z)g=0 does not have a solution g with λ(g)<∞. 相似文献
12.
本文主要研究一类复线性微分差分方程超越亚纯解的唯一性.特别地,假设$f(z)$为复线性微分差分方程: $W_{1}(z)f''(z+1)+W_{2}(z)f(z)=W_{3}(z)$的一个有穷级超越亚纯解,其中$W_{1}(z)$, $W_{2}(z)$, $W_{3}(z)$为增长级小于1的非零亚纯函数并且满足$W_{1}(z)+W_{2}(z)\not\equiv 0$.若$f(z)$与亚纯函数$g(z)$, $CM$分担0,1,$\infty$,则$f(z)\equiv g(z)$或$f(z)+g(z)\equiv f(z)g(z)$或$f^{2}(z)(g(z)-1)^2+g^{2}(z)(f(z)-1)^2=g(z)f(z)(g(z)f(z)-1)$或存在一个多项式$\varphi(z)=az+b_{0}$使得$f(z)=\frac{1-e^{\varphi(z)}}{e^{\varphi(z)}(e^{a_{0}-b_{0}}-1)}$与$g(z)=\frac{1-e^{\varphi(z)}}{1-e^{b_{0}-a_{0}}}$,其中$a(\neq 0)$, $a_{0}$ $b_{0}$均为常数且$a_{0}\neq b_{0}$. 相似文献
13.
对于一个有穷非零复数$q$, 若下列$q$差分方程存在一个非常数亚纯解$f$, $$f(qz)f(\frac{z}{q})=R(z,f(z))=\frac{P(z,f(z))}{Q(z,f(z))}=\frac{\sum_{j=0}^{\tilde{p}}a_j(z)f^{j}(z)}{\sum_{k=0}^{\tilde{q}}b_k(z)f^{k}(z)},\eqno(\dag)$$ 其中 $\tilde{p}$和$\tilde{q}$是非负整数, $a_j$ ($0\leq j\leq \tilde{p}$)和$b_k$ ($0\leq k\leq \tilde{q}$)是关于$z$的多项式满足$a_{\tilde{p}}\not\equiv 0$和$b_{\tilde{q}}\not\equiv 0$使得$P(z,f(z))$和$Q(z,f(z))$是关于$f(z)$互素的多项式, 且$m=\tilde{p}-\tilde{q}\geq 3$. 则在$|q|=1$时得到方程$(\dag)$不存在亚纯解, 在$m\geq 3$和$|q|\neq 1$时得到方程$(\dag)$解$f$的下级的下界估计. 相似文献
14.
15.
Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |