标题： 与偶指数权重相关的正交多项式的逼近 显示英文标题

标题： Approximation by orthonormal polynomials associated with even exponential weights

摘要： 在本文中，我们通过与形式为 e -$\Phi$的指数权函数相关的正交多项式证明了一个定量逼近结果，其中$\Phi$是一个首项系数为正的偶多项式。 这一结果是正交多项式的递推关系和强 Poincaré 不等式的结论。 文章末尾提供了模拟结果，涉及光滑函数、非光滑函数以及高斯情形和双势阱情形。 显示英文摘要

摘要： In this paper, we prove a quantitative approximation result by orthonormal polynomials associated to an exponential weight of the form e -$\Phi$ , where $\Phi$ is an even polynomial with positive leading coefficient. This result is a consequence of a recursion relation for the orthonormal polynomials and of the strong Poincar{\'e} inequality. Simulations are provided at the end of the article, on smooth, non-smooth functions as well as in the Gaussian and the double well case.