Classical And Approximate Sampling Theorem With Several Variables; Studies In The L~p(R~n) And The Uniform Norm

In this paper, making use of the methods of harmonic analysis and numerical analysis,we study the approximate sampling theorem with several variables, and the relationshipbetween the classical sampling theorem with several variables and the approximate samplingtheorem with several variables. And then we estimate the aliasing error of the function inF~p(introduce in section1.3).At last, we prove that the approximate sampling theorem withseveral variables is convergent, i.e. the aliasing error of the function in∧~p(introduce insection3.1) tends to zero in the L~p-norm.