Approximation of functions from generalized Nikolskii Besov classes by entire functions in Lebesgue spaces(in Ukrainian)

Author V. V. Myroniuk, S. Ya. Yanchenko
VetalMyronjuk@ukr.net, Sergiy.Yan@rambler.ru
I

Abstract Exact-order estimates for the approximations of functions of classes $S^{\Omega}_{p,{\theta}}B(\mathbb{R}^d)$ by entire functions with the spectrum of a special form in the space $L_q(\mathbb{R}^d)$ for some relations between the parameters $p$ and $q$, are established.
Keywords approximation; functional class; entire function
Reference 1. Stasyuk S.A., Yanchenko S.Ya. The best Approximation of classes $B^{\Omega}_{p,\theta}$ of function of many variables in the space $L_p(\mathbb{R}^d)$// Zb. Pr. Inst. Mat. NAN Ukr. 2008. V.5, 1. P. 367384. (in Ukrainian)

2. Yanchenko S.Ya. Approximation of classes $B^{\Omega}_{p,\theta}$ of function of many variables by entire functions in the space $L_q(\mathbb{R}^d)$// Ukr. Mat. Zh. 2010. V.62, 1. P. 123135. (in Ukrainian)

3. Bari N.K., Steckin S.B. Best approximations and differential properties of two conjugate functions// Trudy Moskov. Mat. Obsc. 1956. V.5. P. 483522. (in Russian)

4. Amanov T.I. Representation and embedding theorems for the function spaces $S^{(r)}_{p,\theta}B(\mathbb{R}_n)$ and $S^{(r)_*}_{p,\theta}B$ ${(0\leqslant x_j\leqslant 2\pi, j=1,...,n)}$// Trudy Mat. Inst. Steklov. 1965. V.77. P. 534. (in Russian)

5. Nikolskii S.M. Functions with dominant mixed derivative, satisfying a multiple Holder condition// Sibirsk. Mat. Zh. 1963. V.4, 6. P. 13421364. (in Russian)

6. Lizorkin P.I. Generalized Liouville differentiation and the multiplier method in the theory of embeddings of classes of differentiable functions// Trudy Mat. Inst. Steklov. 1969. V.105. P. 89167. (in Russian)

7. Vladimirov V.S. The equations of mathematical physics. M.: Nauka, 1967, 436 p. (in Russian)

8. Lizorkin P.I., Nikolskii S.M. Function spaces of mixed smoothness from the decomposition point of view// Trudy Mat. Inst. Steklov. 1989. V.187. P. 143161. (in Russian)

9. Heping W., Yongsheng S. Approximation of multivariate functions with a certain mixed smoothness by entire functions// Northeast. Math. J. 1995. V.11, 4. P. 454466.

10. Yanchenko S.Ya. Approximation of the classes $S^{r}_{p,\theta}B(\mathbb{R}^d)$ of functions of many variables by entire functions of a special form// Ukr. Mat. Zh. 2010. V.62, 8. P. 11241138. (in Ukrainian)

11. Romanyuk A.S. Approximation of classes of periodic functions of several variables// Mat. Zametki. 2002. V.71, 1. P. 109121. (in Russian)

12. Stasyuk S.A. The best orthogonal trigonometric approximations of classes of periodic functions of several variables $B^{\Omega}_{p,\theta}$// Work Inst. Mat. NAN Ukr. 2002. V.35. P. 195208. (in Ukrainian)

13. Nikolskii S.M. Approximation of function of several variables and imbedding theorems. M.: Nauka, 1969, 480 p. (in Russian)

14. Temlyakov V.N. Approximation of functions with bounded mixed derivative// Trudy Mat. Inst. Steklov. 1986. V.178. P. 1112. (in Russian)

15. Besov O.V., Ilin V.P., Nikolskii S.M. Integral representations of functions and embedding theorems. M.: Nauka, 1996, 480 p.

16. Yanchenko S.Ya. Order estimates of approximation characteristics of classes of functions defined on Rd// Zb. Pr. Inst. Mat. NAN Ukr. 2011. V.8, 1. P. 244262. (in Ukrainian)

Pages 190-202
Volume 39
Issue 2
Year 2013
Journal Matematychni Studii
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