多元函数最佳逼近的精确阶

ON THE PRECISE ORDER OF THE BEST APPROXIMATIONS OF MULTIRARIATE FUNCTIONS

:关于找使得 Ω m( f ,1σ)～ Aσ( f ) (σ→∞ ) .成立的充分条件和必要条件的 Timan问题被解决 ,必要条件是 Ω m( f ,1σ)～Ω m+1( f ,1σ) , (σ→∞ ) .充分条件是 ωmjej ( f ,1σj)～ (ωmj+1ej ( f,1σj) ( σj→∞ ,j=1,2 ,… ,n) .

The Problem of Timan on finding a necessa ry Condition and a sufficient condition fot Ω m(f,1/σ)～A σ(f).(σ→∞) is Solved.The necessary Condition is Ω m(f,1/σ)～Ω m+1 (f,1/σ).(σ →∞) The sufficient contition is [HT4,5]ω m j e j (f,1/σ j)～[HT4,5]ω m j+1 e j (f,1/σ j )(σ j→∞,j=1,2,…,n).