逃避非切向性：朝向受控切向摊销Julia-Carathéodory理论
Escaping nontangentiality: Towards a controlled tangential amortized Julia-Carathéodory theory
摘要：
设$f: D \rightarrow Ω$为复解析函数。Julia商由$f(z)$到$Ω$的边界的距离与$z$到$D.$的边界的距离之间的比率给出。经典Julia-Carathéodory型定理指出，如果在Julia商有界的$D$的边界中存在趋向于$τ$的序列，则函数$f$可以推广到$τ$，使得$f$在$τ$处非切连续且可微，并且$f(τ)$在$Ω.$的边界上。理论，当$D$和$Ω$被视为上半平面时，其对应于受控切向方法的集合上的Julia商的摊销有界性，所谓的$λ$-Stolz区域，以及高阶正则性，包括但不限于高阶可微性，我们使用$γ$ -正则性来测量。应用，包括摄动理论和矩问题。
英文摘要：
Let $f: D \rightarrow Ω$ be a complex analytic function. The Julia quotient is given by the ratio between the distance of $f(z)$ to the boundary of $Ω$ and the distance of $z$ to the boundary of $D.$ A classical Julia-Carathéodory type theorem states that if there is a sequence tending to $τ$ in the boundary of $D$ along which the Julia quotient is bounded, then the function $f$ can be extended to $τ$ such that $f$ is nontangentially continuous and differentiable at $τ$ and $f(τ)$ is in the boundary of $Ω.$ We develop an extended theory when $D$ and $Ω$ are taken to be the upper half plane which corresponds to amortized boundedness of the Julia quotient on sets of controlled tangential approach, so-called $λ$-Stolz regions, and higher order regularity, including but not limited to higher order differentiability, which we measure using $γ$-regularity. Applications are given, including perturbation theory and moment problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
