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| ON n- WIDTHS OF PERIODIC FUNCTIONS |
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Citation： |
Chen Hanlin.ON n- WIDTHS OF PERIODIC FUNCTIONS[J].Chinese Annals of Mathematics B,1991,12(3):272~281 |
| Page view： 932
Net amount： 876 |
Authors： |
Chen Hanlin; |
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| Abstract： |
Let $\[\tilde B_p^{r,1} = \{ f:{f^{(r - 1)}}\]$ is abs. cont. on $I=[a,b]$ is periodic with period H(=b-a)，$\[f({x_1}) = 0,\parallel {f^{(r)}}{\parallel _p} \le 1\} \]$, Where $x_{1}$ is any fixed point in $[a,b]$. The author finds the Kolmogorov, Gel'fand, linear, and Berttrstein n-widths of $\[\tilde B_p^{r,1}\]$ in $L^{P}(I)$ for n odd, $\[1 < p < \infty \]$. The optimal subspaces and operators are also found. |
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