Pervasive function spaces and the best harmonic approximation
โ Scribed by Ivan Netuka
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 384 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0021-9045
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๐ SIMILAR VOLUMES
We show that the set of semi-Lipschitz functions, defined on a quasi-metric space (X, d ), that vanish at a fixed point x 0 # X can be endowed with the structure of a quasi-normed semilinear space. This provides an appropriate setting in which to characterize both the points of best approximation an
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
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, \(X\) ),