论文标题
高斯正交弗洛伊德重量，调制空间和marcinkiewicz-zygmund不平等现象
Gauss Quadrature for Freud Weights, Modulation Spaces, and Marcinkiewicz-Zygmund Inequalities
论文作者
论文摘要
我们研究了弗洛伊德重量的高斯正交正交，并在相关的Sobolev空间家族的功能中得出了最坏情况的错误估计。对于高斯重量，$ e^{ - πx^2} $这些空间与一类调制空间一致，这些空间在（时频）分析中众所周知，也以Hermite空间的名义出现。扩展是针对来自Marcinkiewicz-Zygmund不平等的更通用的节点集。该概括可以解释为高斯正交的稳定性结果。
We study Gauss quadrature for Freud weights and derive worst case error estimates for functions in a family of associated Sobolev spaces. For the Gaussian weight $e^{-πx^2}$ these spaces coincide with a class of modulation spaces which are well-known in (time-frequency) analysis and also appear under the name of Hermite spaces. Extensions are given to more general sets of nodes that are derived from Marcinkiewicz-Zygmund inequalities. This generalization can be interpreted as a stability result for Gauss quadrature.
