发表机构
Clemson University; Zhejiang University of Finance and Economics（克莱姆森大学; 浙江财经大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有限扇形上移位锥形极点近似的精确渐近与维度控制，提出误差界、前导常数及显式表示维度公式，并通过实验验证。
AI 中文摘要
我们研究在闭合单位半径扇形上对 $g(z)z^\alpha(\log z)^m$ 的显式闪电加多项式（LP）近似，其中 $0<\alpha<1$，$m$ 固定，且 $g$ 在附近解析。由于基本的扇形根指数速率已知，我们处理三个更精细的问题。首先，单侧阿贝尔-泊松公式和无极点凹口轮廓给出了分支wise误差界，该误差界对 $(0,1)$ 紧子集中的网格移位一致，并对每个固定的对数幂有效。其次，对于稠密和平衡状态下的 $z^\alpha$，精确的顶点尺度重标度确定了指定移位序列的正有限前导常数。第三，速率匹配的附加表示极点带随后进行多项式压缩，给出显式表示维度 $N+2\sqrt{2\alpha\lambda_\sigma N}+O(1)$，同时保持前 $N$ 个锥形极点不变。略微过分辨率的混合序列也保持精确的前导常数。匹配维度实验（包括凹入扇形）说明了分配。这些精确渐近和维度陈述涉及所述构造，而非扇形极小极大近似或总计算复杂度。
英文摘要
We study explicit lightning-plus-polynomial (LP) approximation of $g(z)z^α(\log z)^m$ on a closed unit-radius sector, where $0<α<1$, $m$ is fixed, and $g$ is analytic nearby. Since the basic sector root-exponential rate is already known, we address three finer questions. First, a one-sided Abel--Poisson formula and a pole-free notched contour give a branchwise error bound that is uniform for grid shifts in compact subsets of $(0,1)$ and valid for every fixed logarithmic power. Second, for $z^α$ in the dense and balanced regimes, an exact vertex-scale rescaling identifies a positive finite leading constant for a specified shifted sequence. Third, a rate-matched band of additional representation poles followed by polynomial compression gives the explicit representation dimension $N+2\sqrt{2αλ_σN}+O(1)$ while leaving the first $N$ tapered poles unchanged. A slightly overresolved hybrid sequence also preserves the exact leading constant. Matched-dimension experiments, including reentrant sectors, illustrate the allocation. These exact-asymptotic and dimension statements concern the stated constructions, not sector minimax approximation or total computational complexity.
