多元函数的最佳逼近递减的逼近阶(英文)

On the Precise Order of Decrease of the Best Approximations of Multivariate Functions

关于找一个必要与充分条件使得ωki1… kimf ,1σi1,… ,1σim～ Yσi1…σim(f ) ,(σij →∞ )成立的 Timan问题被解决 .这条件是ωki1… kim(f ,δi1…δim)～ωki1+ 1,… ,kim+ 1(f ,δi1…δim) ,(δij → 0 )

The problem of Timan on finding a necessary and sufficient condition for ω k i 1 …k i m f, 1σ i 1 ,…,1σ i m ～Y σ i 1 …σ i m (f),(σ i j →∞) is solved. The condition is, ω k i 1 …k i m (f,δ i 1 …δ i m )～ω k i 1 +1,…,k i m+1 (f,δ i 1 …δ i m ),(δ i j →0).