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Estimates of approximations of functions by trigonometric polynomials in spaces with an asymmetric norm and sign-sensitive weight

https://doi.org/10.22405/2226-8383-2024-25-3-177-186

Abstract

In approximation theory, the problems of finding an estimate of the best approximation through the structural properties of the approximated function are well known. The work is devoted to such problems in spaces with an asymmetric norm and sign-sensitive weights.

About the Author

Artem Ivanovich Kozko
Lomonosov Moscow State University; Moscow center of fundamental and applied mathematics
Russian Federation

candidate of physical and mathematical sciences



References

1. Stechkin, S. B. 1949, “On the order of best approximation of continuous functions”, Dokl. Akad. Nauk SSSR. vol. 65 (135), pp. 135–137. (In Russ.)

2. Stechkin, S.B. 1951, “On the order of best approximation of continuous functions”, Izv. Akad. Nauk SSSR Ser. Mat. vol. 15 (3), pp. 219–242. (In Russ.)

3. Timan M. F. 1958, “Inverse theorems of the constructive theory of functions in 𝐿𝑝 spaces

4. (1 ⩽ 𝑝 ⩽ ∞)”, Mat. Sb. N.S. vol 46(88), pp. 125–132. (In Russ.)

5. Gavrilyuk V. T. and Stechkin S. B. 1987, “Approximation of Continuous Periodic Functions by Fourier Sums”, Proc. Steklov Inst. Math. vol 172, pp. 119—142.

6. Babenko A. G. 1998, “An exact Jackson–Stechkin inequality for 𝐿2 -approximation on the interval with the Jacobi weight and on projective spaces”, Izv. Math. vol. 62:6, pp. 1095—1119.

7. Chernykh N. I. 1967, “Jackson’s inequality in 𝐿2”, Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.] vol. 88, pp. 71–74.

8. Аrestov V. V., Chernykh N. I. 1981, “Оn the 𝐿2-approximatioп of periodic function bу

9. trigonometric polуnomials”, Аpproximation and function spaces. Рroc. Inter. Сonf. (Gdansk,

10. . Аmsterdam: North-Hollaпd. pp. 95–43.

11. Kozko A.I., Rozhdestvenskii A.V. 2003, “On Jackson’s inequality for generalized moduli of continuity”, Math. Notes Vol. 73 (5-6), pp. 736–741.

12. Kozko A.I., Rozhdestvenskii A.V. 2004, “On Jackson’s inequality for a generalized modulus of continuity in 𝐿2”, Sb. Math. vol. 195:8, pp. 1073–1115.

13. Kozko A.I. 1998, “Fractional derivatives and inequalities for trigonometric polynomials in spaces with asymmetric norms”, Izvestiya: Mathematics vol. 62 (6), pp. 1189–1206. DOI:

14. 1070/im1998v062n06ABEH000223

15. Kozko A.I. 1998, “Multidimensional inequalities between distinct metrics in spaces with an asymmetric norm”, Sb. Math. vol. 189:9, pp. 1361–1383.

16. Kozko A.I. 1997, “Analogs of the Jackson–Nikol’skii inequalities for trigonometric polynomials in spaces with asymmetric norms”, Math. Notes vol. 61 (5), pp. 574—584. DOI: https://doi.org/10.1007/BF02355078

17. Kozko A.I. 2006, “Completeness of orthogonal systems in asymmetric spaces with sign-sensitive weight”, Journal of Mathematical Sciences, Plenum Publishers (United States), vol. 139 (6), pp. 7151–7164.

18. Kozko A.I. 2002, “On the order of the best approximation in spaces with asymmetric norm and sign-sensitive weight on classes of differentiable functions”, Izv. Math. vol. 66 (1), pp. 103–132. DOI: https://doi.org/10.4213/im373

19. Ramazanov A.-R.K., Ibragimova B.M. 2010, “An asymmetric integral modulus of continuity and an analogue of Jackson’s first theorem”, Bulletin of Dagestan State University. vol 6, pp. 51–54. (In Russ.)

20. Natanson, I. P. 1964, “Constructive function theory. Vol. I. Uniform approximation. Translated by Alexis N. Obolensky.”, New York: Frederick Ungar Publishing Co. IX, 232 p.

21. Korneichuk N. P. 1962, “The exact constant in D. Jackson’s theorem on best uniform

22. approximation of continuous periodic functions”, Doklady Akademii Nauk SSSR vol. 145 (3), pp. 514–515.

23. Korneichuk N. P. 1991, “Exact constants in approximation theory”, Approximation theory Publisher Cambridge ; New York : Cambridge University Press. 452 p.

24. Zhuk V. V. 1982, “Approximation of periodic functions. (Approksimatsiya periodicheskikh funktsij). (Russian)”, Leningrad: Izdatel’stvo Leningradskogo Universiteta. 368 p.


Review

For citations:


Kozko A.I. Estimates of approximations of functions by trigonometric polynomials in spaces with an asymmetric norm and sign-sensitive weight. Chebyshevskii Sbornik. 2024;25(3):177-186. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-3-177-186

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