当前位置: X-MOL 学术Int. J. Math. › 论文详情
Entire functions with prescribed singular values
International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-08-05 , DOI: 10.1142/s0129167x20500755
Luka Boc Thaler

We introduce a new class of entire functions which consists of all F0𝒪() for which there exists a sequence (Fn)𝒪() and a sequence (λn) satisfying Fn(z)=λn+1eFn+1(z) for all n0. This new class is closed under the composition and it is dense in the space of all nonvanishing entire functions. We prove that every closed set V containing the origin and at least one more point is the set of singular values of some locally univalent function in , hence, this new class has nontrivial intersection with both the Speiser class and the Eremenko–Lyubich class of entire functions. As a consequence, we provide a new proof of an old result by Heins which states that every closed set V is the set of singular values of some locally univalent entire function. The novelty of our construction is that these functions are obtained as a uniform limit of a sequence of entire functions, the process under which the set of singular values is not stable. Finally, we show that the class contains functions with an empty Fatou set and also functions whose Fatou set is nonempty.

更新日期:2020-09-18

 

全部期刊列表>>
物理学研究前沿热点精选期刊推荐
科研绘图
欢迎报名注册2020量子在线大会
化学领域亟待解决的问题
材料学研究精选新
GIANT
自然职场线上招聘会
ACS ES&T Engineering
ACS ES&T Water
屿渡论文,编辑服务
阿拉丁试剂right
张晓晨
田蕾蕾
李闯创
刘天飞
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
天合科研
x-mol收录
X-MOL
清华大学
廖矿标
陈永胜
试剂库存
down
wechat
bug