Abstract
We continue the investigation of the approximation characteristics of the spaces \(S_\phi ^p\) introduced earlier. In particular, we establish direct and inverse theorems on the approximation of elements of these spaces. We also determine the exact values of upper bounds of m-term approximations of q-ellipsoids in the spaces \(S_\phi ^q\) in the metrics of the spaces \(S_\phi ^p\).
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REFERENCES
A. I. Stepanets, “Approximation characteristics of spaces S pϕ ,” Ukr. Mat. Zh., 53, No. 3, 392-416 (2001).
S. B. Stechkin, “On the absolute convergence of orthogonal series,” Dokl. Akad. Nauk SSSR, 102, No. 1, 37-40 (1955).
A. I. Stepanets, “Mean square rate of convergence of orthogonal series,” Ukr. Mat. Zh., 39, No. 5, 606-611 (1987).
A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
A. N. Kolmogorov, “Ñber die beste Annäherung von Funktionen einer gegebenen Funktionenklass,” Ann. Math., 37, No. 1, 107-110 (1936).
V. M. Tikhomirov, Some Problems in Approximation Theory [in Russian], Moscow University, Moscow (1976).
K. I. Babenko, “On the approximation of periodic functions of many variables by trigonometric polynomials,” Dokl. Akad. Nauk SSSR, 132, No. 2, 247-250 (1960).
K. I. Babenko, “On the approximation of one class of periodic functions of many variables by trigonometric polynomials,” Dokl. Akad. Nauk SSSR, 132, No. 5, 982-985 (1960).
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Stepanets, A.I. Approximation Characteristics of the Spaces S ϕ p in Different Metrics. Ukrainian Mathematical Journal 53, 1340–1374 (2001). https://doi.org/10.1023/A:1013307912783
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DOI: https://doi.org/10.1023/A:1013307912783