共查询到20条相似文献,搜索用时 176 毫秒
1.
主要考虑了Dirichlet空间中的正交函数.主要结论表明单位圆盘中的一个解析自映射是Dirichlet空间中的正交函数,当且仅当其所对应的计数函数是本质径向的;当且仅当其所对应的诱导测度是径向的.作为主要结论的一个应用,给出了单位圆盘上的单叶解析函数和闭单位圆盘上的解析函数是Dirichlet空间中正交函数的完全刻画. 相似文献
2.
A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points. 相似文献
3.
Cauchy-Stieltjes积分和面积平均p叶函数 总被引:1,自引:0,他引:1
本文研究由Cauchy-Stieltjes积分形成的函数空间Fα.首先给出这个空间的一个等价定义,然后研究面积平均p叶函数的对数函数和这个函数空间的关系,最后对单叶函数的情形做进一步的讨论.根据这种研究,我们得到了有界单叶函数的系数增长估计,这是目前最好的结果. 相似文献
4.
Using the Faber polynomials, we obtain coefficient expansions for analytic bi-close-to-convex functions and determine coefficient estimates for such functions. We also demonstrate the unpredictable behavior of the early coefficients of subclasses of bi-univalent functions. A function is said to be bi-univalent in a domain if both the function and its inverse map are univalent there. 相似文献
5.
关于某类解析函数的星象性和Ruscheweyh的一个问题 总被引:2,自引:0,他引:2
本文引入了一个涉及Ruscheweyh导数的解析函数子类,应用微分从属方法和Carlson-Shaffer算子讨论了它的从属关系和偏差定理;其次,应用单叶函数的性质和一个微分不等式研究了它的星象性条件和覆盖定理,最后,部分地解决了Ruscheweyh的一个问题。 相似文献
7.
Jian-Lin Li 《Journal of Mathematical Analysis and Applications》1999,230(2):375
In this note we show that Ruscheweyh's multiplier conjecture is true in several special cases. The results obtained here are closely related to the partial sums of certain analytic functions defined by means of univalent functions. We also answer a question of Ponnusamy concerning thenth partial sums of certain univalent functions. 相似文献
8.
李万社 《纯粹数学与应用数学》1993,9(1):90-94
1980年,P.Duren和G.Schober引入了非零单叶函数族S_0,f∈S_0是指f(z)在单位园盘内单叶解析,恒不等于零并且用条件f(0)=1正规化。在后来的一系列文章中,他们研究了S_0的闭凸包HS_0中的线性极值问题。设ψ是S_0上的实值连续凸泛函,本文研究了凸极值问题maxψ(f)f∈S_0,得到极值函数值域及其不取弧的一些性质,这些结果包含了P.Duren和G.Schober的结果。 相似文献
9.
According to the Charzynski-Tammi conjecture, the symmetrized Pick function is extremal in the problem on the estimate for the nth Taylor coefficient in the class of holomorphic univalent functions close to the identical one. In this paper we find the exact value of M 4 such that the symmetrized Pick function is locally extremal in the problem on the estimate for the 4th Taylor coefficient in the class of holomorphic normalized univalent functions, whose module is bounded byM 4. 相似文献
10.
We apply the capacity and symmetrization methods to distortion theorems for analytic functions in an annulus. We show that the classical Teichmüller estimate for the capacity of a doubly-connected domain yields a series of the already known and new inequalities for univalent functions. In particular, we supplement the results of Grötzsch, Duren, and Huckemann. Using the dissymmetrization of condensers we establish sharp estimates for local distortion and the distortion of level curves in n ≥ 2 symmetric directions. In terms of Robin functions we give an analog of the Nehari inequality: some general distortion theorem for several points taking into account the boundary behavior of the function and describing the cases of equalities. As a corollary we give analogs of some inequalities of Solynin, Pommerenke, and Vasil’ev that were obtained previously for univalent and bounded functions in a disk. We prove a distortion theorem that involves the Schwarzian derivatives at symmetric points on the unit circle. 相似文献
11.
In the class of univalent bounded normalized holomorphic functions in the unit disk, we give an asymptotic estimate for the coefficients when the uniform norm of the modulus of the function tends to infinity. 相似文献
12.
Simon DAVIS 《数学学报(英文版)》2012,28(6):1233-1236
The relation between Diff(S 1)/S 1 and the space of univalent analytic functions on the disk is elucidated and shown to provide upper bounds for the volumes of exhaustive approximations to an analytic submanifold of an infinite-dimensional space. The maximum magnitudes of the coefficients in the series expansions of univalent superanalytic functions on the superdisk are inferred. 相似文献
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In this paper, we introduce new subclasses of analytic and univalent functions and establish certain results concerning the quasi-Hadamard product of functions in these subclasses. Our result includes several previous known results as special cases. 相似文献
15.
S. R. Nasyrov 《Mathematical Notes》2007,82(5-6):798-802
We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f (k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane. 相似文献
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17.
New applications of generalized condensers with two or more plates are considered. Based on one and the same approach and
simplest properties of such condensers, boundary distortion theorems for analytic univalent functions bounded in a disk are
established, as well as bounds for certain combinations of coefficients in expansions of such functions, inequalities for
polynomials, and theorems on extremal decompositions of the complex sphere. Part of the results obtained contains new information
on the Schwarzian derivative of a regular univalent function. Bibliography: 21 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 52–75. 相似文献
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19.
Kunyu Guo 《Journal of Functional Analysis》2011,261(1):51-68
In this paper, we study the Rudin orthogonality problem on the Bergman space, which is to characterize those functions bounded analytic on the unit disk whose powers form an orthogonal set in the Bergman space of the unit disk. We completely solve the problem if those functions are univalent in the unit disk or analytic in a neighborhood of the closed unit disk. As a consequence, it is shown that an analytic multiplication operator on the Bergman space is unitarily equivalent to a weighted unilateral shift of finite multiplicity n if and only if its symbol is a constant multiple of the n-th power of a Möbius transform, which was obtained via the Hardy space theory of the bidisk in Sun et al. (2008) [10]. 相似文献