The problem of recovering a moment-determinate multivariate function $f$ via its moment sequence is studied. Under mild conditions on $f$, the point-wise and $L_1$-rates of convergence for the proposed constructions are established. The cases where $f$ is the indicator function of a set, and represents a discrete probability mass function are also investigated. Calculations of the approximants and simulation studies are conducted to graphically illustrate the behavior of the approximations in several simple examples. Analytical and simulated errors of proposed approximations are recorded in Tables 1-3.

翻译：本文研究通过矩序列恢复矩确定多元函数$f$的问题。在关于$f$的温和条件下，建立了所构造方法的逐点收敛速率与$L_1$收敛速率。同时探讨了$f$为集合指示函数及离散概率质量函数的情形。通过若干简单示例，计算近似函数并开展仿真研究，以图形方式展示近似行为的特征。所提近似的解析误差与模拟误差记录于表1-3中。