Superresolution of principal semi-algebraic sets

12 Aug 2020  ·  Putinar Mihai ·

The H\"older 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.

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Classical Analysis and ODEs Functional Analysis