Approximation Characteristic Of The General Sobolev Space With Worst Case Setting

In the present article, we define the general Sobolev space S pr(Τ)( 1≤p≤∞) in the S q(Τ) by Fourier series, and investigate the approximation characteristic of the general Sobolev space in worst case setting. Then, the exact order of Kolmogorov n-width and linear n-width of the general Sobolev space S pr(Τ) in the S q(Τ) are determined, which based on functional analysis, algebraic theory, distribution method and technology, namely (1)Let 1≤p,q≤∞, r > max(0 ,q1≤1p), then (?)Where BS pr(Τ)is the ball of the S pr(Τ).