科研之友
微信
新浪微博
Facebook
分享链接
摘要
The convolution properties are discussed for the complex-valued harmonic functions on the unit disk constructed from the harmonic shearing of the analytic function , where and are real numbers. For any real number and a harmonic function , define an analytic function by . Let and be real numbers, and and be locally univalent and sense-preserving harmonic functions such that . It is shown that the convolution is univalent and convex in the direction of , provided it is locally univalent and sense-preserving. Also, local univalence of the above convolution is shown when f and F have specific analytic dilatations. Furthermore, if and both the analytic functions and are convex, then the convolution is shown to be convex. These results extend the work of Dorff et al. (Complex Var Elliptic Equ 57(5):489-503, 2012) to a larger class of functions.
- 出版日期2018-4
