ISSN:
1432-0940
Keywords:
41A46
;
41A15
;
n-Widths
;
Exact estimates
;
Strong asymptotic estimates
;
Classes of periodic functions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let $$\tilde W_p^r : = \left\{ {f\left| {f \in C^{r - 1} } \right.} \right.\left[ {0,2\pi } \right],f^{(i)} (0) = f^{(i)} (2\pi ),i = 0, \ldots ,r - 1,f^{(r - 1)}$$ , abs. cont. on [0, 2π] andf (r)∈L p[0, 2π]}, and set $$\tilde B_p^r : = \left\{ {f\left| {f \in \tilde W_p^r ,} \right.\left\| {f^{(r)} } \right\|_p \leqslant 1} \right\}$$ . We find the exact Kolmogrov, Gel'fand, and linearn-widths of $$\tilde B_p^r$$ inL p forn even and allp∈(1, ∞). The strong asymptotic estimates forn-widths of $$\tilde B_p^r$$ inL p are also obtained.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01279021