A Schwarz Lemma at the Boundary of Hilbert Balls

In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B′in separable complex Hilbert spaces H and H′, respectively. It is found that if the mapping f ∈ C~(1+α)at z_0∈ ?B with f(z_0) = w_0∈ ?B′, then the Fr′echet derivative operator Df(z_0) maps the tangent space Tz_0(?B~n) to Tw_0(?B′), the holomorphic tangent space T_(z_0)~(1,0)(?B~n) to T_(w_0)~(1,0)(?B′),respectively.     

A Generalized Schwarz Lemma

In this paper,we establish a boundary Schwarz Lemma for holomorphic mapping on the generalized complex ellipsoid in Cn.     

A Schwarz Lemma for the Symmetrized Bidisc

Let be an analytic function from D to the symmetrized bidisc We show that if (0) = (0,0) and () = (s, p) in the interiorof , then Moreover, the inequality is sharp: we give an explicit formulafor a suitable in the event that the inequality holds withequality. We show further that the inverse hyperbolic tangentof the left-hand side of the inequality is equal to both theCaratheodory distance and the Kobayashi distance from (0,0)to (s, p) in int      

Schwarz引理的一个注记

本文中,基于幅角原理和同论理论紧密联系的想法,我们对单复变中经典的Sdlwarz引理给出了一个新的证明.同时,运用同样的方法,我们把Schwarz引理推广到亚纯函数和多连通区域的情形.     

A Refined Schwarz Lemma for the Spectral Nevanlinna-Pick Problem

The spectral Nevanlinna–Pick problem asks for necessary and sufficient conditions for the existence of a holomorphic map from the unit disc to the set of $n\times n$ complex matrices with spectral radius less than 1, that interpolates given data. Some versions of the Schwarz lemma, obtained by Ransford and Nokrane, and by Bharali, provide necessary conditions. We prove a refined version of their results, which makes it possible to treat problems with more than two interpolation points.     

A Boundary Schwarz Lemma for Holomorphic Mappings on the Polydisc

The authors prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary Schwarz lemma.     

边界型Schwarz引理

Schwarz引理是复分析中最重要的定理之一,本文给出了边界型Schwarz引理.     

Schwarz Lemma in infinite-dimensional spaces

We state and prove an extension of the Schwarz Lemma that involves infinite-dimensional spaces. Our generalized version contains some known variations of this classical result in geometric function theory. We derive our extension in the context of the Minkowski functional.     

关于全纯映照模的Schwarz引理一点注记

记DC为单位圆盘,B~k C~k为开欧氏单位球,Ω是C~k(或C)中的域.记H_n(D,Ω)为满足一定条件的全纯映照族(或函数族)的全体.作者证明了若,∈Hn(D,D),则|f′(z)|≤(n|z|~(n-1))/(1-|z|~(2n))(1-|f|(z|~2),z∈DD同时,对Hn(D,B~k)中映照的模也得到类似的结果.该结论推广了Pavlovic的相应结果.     

Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广

对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计.     

On a Schwarz Lemma for Bounded Symmetric Domains

We develop a new systematic approach to the Boussinesq (Bsq) hierarchy based on elementary algebraic methods. In particular, we recursively construct Lax pairs for the Bsq hierarchy by introducing a fundamental polynomial formalism and establish the basic algebro -geometric setting including associated Burchnall - Chaundy curves, Baker - Akhiezer functions, trace formulas, and Dubrovin - type equations for Dirichlet and Neumann divisors.     

Schwarz引理的推广及其应用

引入Schwarz引理的一个最常见的推广定理,并且作出了详细的证明.同时以引理形式介绍了一个实用的复数性质,并且利用这两个引理,给出了开圆盘内解析函数的的实部,虚部以及模的估计式.     

A Schwarz Lemma for Harmonic Mappings Between the Unit Balls in Real Euclidean Spaces

The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball centered at origin can be controlled. This extends the related result proved by Chen in complex plane.     

Dirichlet Problem,Univalency and Schwarz Lemma for Biharmonic Mappings

In this paper, we shall discuss the family of biharmonic mappings for which the maximum principle holds. As a consequence of our study, we present Schwarz Lemma for certain class of biharmonic mappings. Also we discuss the univalency of certain class of biharmonic mappings.     

A Geodesic Between the Hilbert Basis Theorem and Gordan''''s Lemma

Gordan's Lemma and Hilbert Basis theorem, both merging from establishing thefinite generation of invariants, are proved in one combinatorial set up, namely, thesemigroup N~n     

A note on the Kobayashi-Royden metric for real ellipsoids

We give a proof of the fact proven by L.D. Kay that the Kobayashi-Royden metric of a real ellipsoid (of dimension at least ) at is hermitian exactly when the ellipsoid is the ball. The proof given by us is much simpler and shorter than that of Kay although it is based on the same results.

     

拟凸域上沿某些方向的边界 Schwarz 引理*

本文直接利用全纯映照的性质研究边界Schwarz引理,建立了拟凸域上沿某些满足正定条件的方向的边界Schwarz引理. 文章推广了强拟凸域情形的主要结果,但是证明的方法是不一样的.     

Schwarz Lemma and Hartogs Phenomenon in Complex Finsler Manifold

The authors prove the Schwarz lemma from a compact complex Finsler manifold to another complex Finsler manifold and any complete complex Finsler manifold with a non-positive holomorphic curvature obeying the Hartogs phenomenon.