论文标题
关于多序分析函数的无关
On the univalence of polyanalytic functions
论文作者
论文摘要
一个连续的复杂值函数$ f $在域中$ d \ subseteq \ mathbf {c} $是订单$α$的多分析，如果满足$ \ partial^α_ {\ oftial^α_ {\ overline {z}}} f = 0 $F(z)={\displaystyle\sum\limits_{0}^{n-1}}\overline{z}^{k}A_{k}(z)$, where each $A_k$ is an analytic function$.$ In this paper, we prove the existence of a Landau constant for Poly-analytic functions and the special Bi-analytic case.我们还建立了Bohr的不平等，用于将$ U $映射到$ u $中的聚安分析和双分析功能。此外，我们对多分析映射类别的Arclength进行了估计，并考虑了最小化订单$ p $的矩的问题。
A continuous complex-valued function $F$ in a domain $D\subseteq\mathbf{C}$ is Poly-analytic of order $α$ if it satisfies $\partial^α_{\overline{z}}F=0.$ One can show that $F$ has the form $F(z)={\displaystyle\sum\limits_{0}^{n-1}}\overline{z}^{k}A_{k}(z)$, where each $A_k$ is an analytic function$.$ In this paper, we prove the existence of a Landau constant for Poly-analytic functions and the special Bi-analytic case. We also establish the Bohr's inequality for poly-analytic and bi-analytic functions which map $U$ into $U$. In addition, we give an estimate for the arclength over the class of poly-analytic mappings and consider the problem of minimizing moments of order $p$.
