Research in approximation theory in Russia dates back to P. L. Chebyshev's memoir ``The orie des me canismes connus sous le nom de paralle logrammes'' (Me m. Pre s. Acad. Imp. Sci. Pe tersb. Divers Savants, 1854, VII, 539 568). This memoir posed the problem of the best approximation of functions by
The Theory of Best Approximation of Functions
β Scribed by V.L. Goncharov
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 301 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0021-9045
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π SIMILAR VOLUMES
The object of this paper is to prove the following theorem: Let \(Y\) be a closed subspace of the Banach space \(X,(S, \Sigma, \mu)\) a \(\sigma\)-finite measure space, \(L(S, Y)\) (respectively, \(L(S, X)\) ) the space of all strongly measurable functions from \(S\) to \(Y\) (respectively, \(X\) ),
Let \(\xi\) be an irrational number with simple continued fraction expansion \(\xi=\left[a_{0} ; a_{1}, a_{2}, \ldots, a_{i}, \ldots\right]\). Let the \(i\) th convergent \(p_{i} / q_{i}=\left[a_{0} ; a_{1}, a_{2}, \ldots, a_{i}\right]\). Let \(\mu=\) \(\left|\left[0 ; a_{n+2}, a_{n+3}, \ldots\right