Some extremal problems in the Orlicz spaces(in Ukrainian)

Author
A. L. Shidlich, S. O. Chaichenko
Institute of Mathematics of Ukrainian National Academy of Sciences, Donbas State Pedagogical University
Abstract
We obtained the exact values of analogues of the best $n$-term approximations and the basis widths in the Orlicz spaces $L_M(\mathbb{A};d\mu)$ of classes of non-negative functions, which can be represented as the product of a fixed function and functions from the unit balls of the spaces $L_p(\mathbb{A};d\mu)$ and $L_M(\mathbb{A};d\mu)$, respectively.
Keywords
Orlicz spaces; best n-term approximations; basis widths
Reference
1. Stechkin S.B. On absolute convergence of orthogonal series// Dokl. Akad. Nauk SSSR. 1955. V.102, 1. P. 3740. (in Russian)

2. Stepanets A.I., Shidlich A.L. Best approximations of integrals by integrals of finite rank// J. Approx. Theory. 2010. V.162. P. 323348.

3. Stepanets A.I., Shidlich A.L. Extremal problems for integrals of nonnegative functions// Izv. Ross. Akad. Nauk Ser. Mat. 2010. V.74, 3. P. 169224. (in Russian)

4. De Vore R. Nonlinear approximation// Acta Numer. 1998. V.7. P. 51150.

5. Romanyuk A.S. Best M-term trigonometric approximations of Besov classes of periodic functions of several variables// Izv. Ross. Akad. Nauk Ser. Mat. 2003. V.67, 2. P. 61100. (in Russian)

6. Stepanets A.I. Extremal problems of approximation theory in linear spaces// Ukrain. Mat. Zh. 2003. V.55, 10. P. 13781410. (in Russian)

7. Shidlich A.L., Chaichenko S.O. Approximative properties of diagonal operators in Orlicz spaces// arXiv preprint. 2014. arXiv:1405.1542. 11 p.

8. Shidlich A.L., Chaichenko S.O. On some inequalities of Chebyshev type, in press.

9. Shidlich A.L., Chaichenko S.O. On some inequalities of Chebyshev type// arXiv preprint. 2014. arXiv:1405.1256. 6 p.

Pages
21-32
Volume
42
Issue
1
Year
2014
Journal
Matematychni Studii
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