The Hölder continuity of the truncated moment map of a shade function in Euclidean space is established in the vicinity of a principal semi-algebraic set. The proof combines volume bounds of semi-algebraic sets and convex optimization methods. The main estimate is applied to a potential type transform specific to two real variables, for perturbations of quadrature domains.

中文翻译：

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主半代数集的超分辨率

欧几里得空间中阴影函数的截断矩图的Hölder连续性是在一个主要的半代数集附近建立的。该证明结合了半代数集的体积边界和凸优化方法。主要估计应用于特定于两个实变量的潜在类型转换，以用于正交域的扰动。