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Exact and asymptotic estimates forn-widths of some classes of periodic functions (1992)

Chen, Han-lin ; Li, Chun

Springer

Constructive approximation 8 (1992), S. 289-307

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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

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