50余年来的数学科研工作成果综述

1945-2001年主要研究领域为组织分析、渐近分析、函数逼近论、计算方法与计算组合数学。这篇自述报告只就高维渐近积分定理、算子半群理论第一指数公式的量化定理、大范围收敛迭代方法、快速振荡函数积分的渐近展开、Gould-Hsu反演公式、广义Mǒbius反演理论、广义Stirling数的统一研究等成果略作介绍。

A self-explanatory survey on some of mathematical research works and findings in the years 1945-2001

This is a self explanatory survey article in which some of Hsu's mathematical works and findings achieved in the past 50 years have been briefly described. The topics and titles of Hsu's works and results some of which were frequently quoted include the following contents: (1) Multidimensional asymptotic integration theorems; (2) Refinement of the first exponential formula in the theory of semi groups; (3) Iteration method with global convergence; (4) Asymptotic expansion of the integration of rapidly oscillating functions; (5) Gould Hsu's inversion formulae; (6) Generalized Mbius inversion theory; (7) A unified treatment of generalized Stirling numbers.