共查询到20条相似文献,搜索用时 0 毫秒
1.
Ian Graham Hidetaka Hamada Gabriela Kohr Mirela Kohr 《Journal d'Analyse Mathématique》2008,105(1):267-302
In this paper, we define the notion of asymptotic spirallikeness (a generalization of asymptotic starlikeness) in the Euclidean
space ℂ
n
. We consider the connection between this notion and univalent subordination chains. We introduce the notions of A-asymptotic spirallikeness and A-parametric representation, where A ∈ L(ℂ
n
, ℂ
n
), and prove that if
dt < ∞ (this integral is convergent if k
+(A) < 2m(A)), then a mapping f ∈ S(B
n
) is A-asymptotically spirallike if and only if f has A-parametric representation, i.e., if and only if there exists a univalent subordination chain f(z, t) such that D f(0, t) = e
At
, {e
−At
f(·, t)}
t≥0 is a normal family on B
n
and f = f(·, 0). In particular, a spirallike mapping with respect to A ∈ L(ℂ
n
, ℂ
n
) with
dt < ∞ has A-parametric representation. We also prove that if f is a spirallike mapping with respect to an operator A such that A + A* = 2I
n
, then f has parametric representation (i.e., with respect to the identity). Finally, we obtain some examples of asymptotically spirallike
mappings.
Partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A9221.
Partially supported by Grant-in-Aid for Scientific Research (C) no. 19540205 from Japan Society for the Promotion of Science,
2007.
Partially supported by Romanian Ministry of Education and Research, CEEX Program, Project 2-CEx06-11-10/2006. 相似文献
2.
Let B
n
be the unit ball in with respect to an arbitrary norm. We obtain sharp growth and covering theorems for parabolic starlike mappings on B
n
as well as coefficient estimates, and consider various examples. 相似文献
3.
4.
Mathematische Zeitschrift - 相似文献
5.
We give some theorems on algebraic dependence of meromorphic mappings in several complex variables into complex projective spaces. 相似文献
6.
Letf(z, t) be a subordination chain fort ∈ [0, α], α>0, on the Euclidean unit ballB inC
n. Assume thatf(z) =f(z, 0) is quasiconformal. In this paper, we give a sufficient condition forf to be extendible to a quasiconformal homeomorphism on a neighbourhood of
. We also show that, under this condition,f can be extended to a quasiconformal homeomorphism of
onto itself and give some applications.
Partially supported by Grant-in-Aid for Scientific Research (C) no. 14540195 from Japan Society for the Promotion of Science,
2004. 相似文献
7.
F. H. Szafraniec 《Monatshefte für Mathematik》1986,101(1):59-66
We show how the reproducing kernel Hilbert space approach to some holomorphic interpolation problems can be utilized to proveboundedness of their solutions. The goal is two-fold: i) to propose a several variable analogue of the classical Pick-Nevanlinna theorem, ii) to display that a simple argumentation may be carried on in this case, which, though still in a Hilbert space context, avoids any use of operator theory. 相似文献
8.
In this paper, we give a uniqueness theorem for meromorphic mappings from ? n into ? N (? ) with rank≥μ regardless of multiplicities. 相似文献
9.
10.
11.
Sergey E. Stepanov 《Annals of Global Analysis and Geometry》1995,13(3):239-249
This paper is devoted to the study of the global theory of certain mappings between Riemannian manifolds. We generalize results by Vilms, Yano and Ishihara, and study in detail projective, umbilical and harmonic maps.The work of the author was supported by RBRF, grant 94-01-01595 (Russia). 相似文献
12.
Science China Mathematics - In this paper, we study some extremal problems for the family $$S_g^0(mathbb{B}_X)$$ of normalized univalent mappings with g-parametric representation on the unit ball... 相似文献
13.
The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking account of multiplicities of order k in counting functions and a uniqueness theorem for meromorphic mappings sharing 2n + 2(n ≥ 2) hyperplanes in general position, which improve and extend some earlier work. 相似文献
14.
研究了Cn中单位多圆柱上星形映射在某方向上精确的偏差定理.给出了复Banach空间单位球的某方向上精确的偏差的上界,同时给出了下界的猜测. 相似文献
15.
16.
H. Hamada 《Journal of Mathematical Analysis and Applications》2011,381(1):179-186
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form f(z,t)=etAz+?, where A∈L(Cn,Cn) has the property m(A)>0. Here m(A)=min{R〈A(z),z〉:‖z‖=1}. We also give sufficient conditions for g(z,t)=L(f(z,t)) to be polynomially bounded, where f(z,t) is an A-normalized polynomially bounded Loewner chain solution to the Loewner differential equation. 相似文献
17.
18.
In this paper, the refining growth and covering theorems for f are established, where f is a quasi-convex mapping of order α and x = 0 is a zero of order k + 1 of f(x) − x. As an application, we obtain the upper and lower bounds on the distortion theorem of f(x) defined on the unit polydisc of ℂ
n
. The upper bound of the distortion theorem for f(x) defined on the unit ball of a complex Banach space is also given. Our results extend the growth and distortion theorems
for convex functions of one complex variable to quasi-convex mappings of several complex variables. 相似文献
19.