论文标题
关于猜想的一些建议：“使用ChristOffel-Darboux内核拖运的半代数近似”
Some suggestions concerning the conjecture in: 'Tractable semi-algebraic approximation using Christoffel-Darboux kernel'
论文作者
论文摘要
在使用ChristOffel-Darboux内核的“可拖动半代数近似”中$ l^1 $ norm中的$ d $的内核可以改善更多常规功能。在这里，我们将证明，对于半代数和可定义的函数，可以将结果加强到$ l^\ infty $ norm中的合理近似率。
In 'Tractable semi-algebraic approximation using Christoffel-Darboux kernel' Marx, Pauwels, Weisser, Henrion and Lasserre conjectured, that the approximation rate $\mathcal O(\frac 1 {\sqrt(d)})$ of a Lipschitz functions by a semi-algebraic function induced by a Christoffel- Darboux kernel of degree $d$ in the $L^1$ norm can be improved for more regular functions. Here we will show, that for semi-algebraic and definable functions the results can be strengthened to a rational approximation rate in the $L^\infty$ norm.
