| 徐庆华,刘太顺.正规化双全纯映照的增长和掩盖定理[J].数学年刊A辑,2009,30(2):213~220 |
| 正规化双全纯映照的增长和掩盖定理 |
| On the Growth and Covering Theorem for Normalized Biholomorphic Mappings |
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| DOI： |
| 中文关键词: k 1阶零点 增长和掩盖定理 β型螺形映照族及其子族 |
| 英文关键词:Zero of order k + 1, Growth and covering theorems, The class of
spirallike mappings of type and its subclasses |
| 基金项目:国家自然科学基金，教育部高等学校博士学科点专项科研基金，江西省自然科学基金，江西师范大学博士专项研究资助的项目 |
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| 中文摘要: |
| 在一般复Banach空间的单位球上引入正规化全纯映照族Mg,考虑满足条件(Df(x))-f(x)∈M9的正规化局部双全纯映照f(其中x=0是f(x)-x的k+1阶零点)并得到其增长和掩盖定理.所得结果统一和推广了许多已知结论. |
| 英文摘要: |
| Let $X$ be a complex Banach space with norm $\|\cdot\|$, $B$ be the
unit ball in $X$. This introduces a class of holomorphic
mappings $\widehat{\mathcal{M}_g}$ on $B$. Let $f(x)$ be a
normalized locally biholomorphic mapping on $B$ such that
$({\rm D}f(x))^{-1}f(x)\in \widehat{\mathcal{M}_g}$ and $f(x)-x$ has a
zero of order $k+1$ at $x=0$. The growth and covering theorems
for $f(x)$ are obtained. These results include and generalize many known results. |
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