最佳混合范数逼近

THE BEST MIXED-NORM APPROXIMATION

本文研究了两变量函数 f(x,y)用单变量函数 g(x)作混合范数逼近问题,即求g~*(x)∈G,G 是一 Haar 子空间,使(?)integral from Y|f(x,y)-g~*(x)|dμ=(?)integral from Y|f((?),y)-g(x)|dμ我们建立了包括交错定理、de la Vallee Poussin 定理、唯一性定理和强唯一性定理在内的 Chebyshev 逼近理论。

In this paper,we study the problem of mixed-norm approximation tobivariate functions by one variate function,i.e.minimizing the experission(?)integral from Y|f(x,y)-g(x)|dyover G,G is a Haar subspaceWe establish the main theoremsin the Chebyshev theory,which includethe theorems of alternation,de La Vall e Poussin,uniqueness and,stronguniqueness.