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- Title
Inequalities between the best approximations and homogenizations of moduli of continuity in the space L.
- Authors
Shabozov, M. Sh.; Yusupov, G. A.
- Abstract
The article discusses the exact inequalities relating the best approximations of periodic differentiable functions by trigonometric polynomials and order moduli of continuity in linear spaces. It provides the function of the space of the Lebesque measurable periodic real functions having finite norms. It also denotes the function of the subspace of all trigonometric polynomials at a degree to be associated with the functions of Fourier expansion. The value of the approximation by elements of the subspace is given as illustrated in a formula. A formula is also given for solving the extremal problems of the theory of approximation of differentiable periodic functions of trigonometric polynomials on in spaces within the Jackson-Stechkin-type inequalities.
- Subjects
MATHEMATICAL inequalities; MODULI theory; DIFFERENTIAL inequalities; EXTREMAL problems (Mathematics); RADON integrals; FINITE differences; FINITE fields; FINITE model theory; TRIGONOMETRY; POLYNOMIALS; APPROXIMATION theory; INVARIANT subspaces
- Publication
Doklady Mathematics, 2010, Vol 82, Issue 3, p892
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562410060141