IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

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 $d _ n(\Delta^s+W^r _ {p,\alpha})L _ q^{lin},s=0,1,\ldots,r+1$.

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