Generalized M?bius Inversion with Applications to Integral Equations and Interpolation Process——In Memory of the late Professor Loo-Keng Hua(华罗庚)

Abstract:

      The object of this expository paper is to establish a kind of generalized M?bius-Rota inversion formula by the aid of non-standard analysis. Certain constructive applications to Volterra type integral equations and to equidistant smooth interpolation process are expounded in some detail. Moreover, some of our earlier results (cf. [1] ,[2] ,[4]) are refined and improved.