## Kolmogorov and linear widths of weighted Sobolev-type classes on a finite interval II

**A 2000 Preprint by
V. Konovalov and
D. Leviatan
**

- 2000:30
Let

*I*be a finite interval, $r\in{\mathbb{N}}$ and $\rho(t)=\textrm{dist}\{t,\delta{I}\}$, $t\in{I}$. Denote by $\Delta^s+W^r _ {p,\alpha},0\leq{\alpha}<\infty$, the class of functions*x*on*I*with the seminorm $\|x^{(r)}\rho^\alpha\|L _ p\leq1$ for which $\Delta^s _ \tau{x},\tau>0$, is nonnegative on*I.*We obtain two-sided estimates of the Kolmogorov widths $d _ n(\Delta^s+W^r _ {p,\alpha})L _ q$ and of the linear widths $d _ n(\Delta^s+W^r _ {p,\alpha})L _ q^{lin},s=0,1,\ldots,r+1$.