We obtain an exact-order estimate for the best m-term approximation of the classes \( B_{\infty, \theta }^r \) of periodic functions of many variables by polynomials in the Haar system in the metric of the space L q , 1 < q < ∞.
Similar content being viewed by others
References
V. N. Temlyakov, “Nonlinear methods of approximation,” Found. Comput. Math., 3, No. 1, 33–107 (2003).
A. S. Romanyuk, “The best M-term trigonometric approximations of the Besov classes of periodic functions of many variables,” Izv. Ros. Akad. Nauk, Ser. Mat., 67, No. 2, 61–100 (2003).
A. S. Romanyuk and V. S. Romanyuk, “Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables,” Ukr. Mat. Zh., 62, No. 4, 536–551 (2010); English translation: Ukr. Math. J., 62, No. 4, 612–629 (2010).
V. N. Temlyakov, “Approximation of functions with bounded mixed derivative,” Tr. Mat. Inst. Akad. Nauk SSSR, 178, 1–112 (1986).
B. S. Kashin and A. A. Saakyan, Orthogonal Series [in Russian], AFTs, Moscow (1999).
V. N. Temlyakov, “The best m-term approximation and greedy algorithms,” Adv. Comput. Math., 8, No. 3, 249–265 (1998).
V. N. Temlyakov, “Nonlinear m-term approximation with regard to the multivariate Haar system,” East J. Approxim., 4, No. 1, 87–106 (1998).
A. V. Andrianov and V. N. Temlyakov, “Best m-term approximation of functions from classes \( M\,W_{q,a}^r \),” Approxim. Theory, 1, 7–14 (1998).
A.V. Andrianov, “Approximation of functions from the classes \( M\,H_p^r \) by the Haar polynomials,” Mat. Zametki, 66, No. 3, 323–335 (1999).
P. Oswald, “On N-term approximations in the Haar system in H s-norms,” Sovr. Mat. Fund. Napr., 25, 106–125 (2007).
S. A. Stasyuk, “Approximation of functions of many variables from the classes \( H_p^\Omega \) by polynomials in the Haar system,” Anal. Math., 35, No. 4, 257–271 (2009).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 549–555, April, 2011.
Rights and permissions
About this article
Cite this article
Stasyuk, S.A. Best m-term approximation of the classes\( B_{\infty, \theta }^r \) of functions of many variables by polynomials in the haar system. Ukr Math J 63, 638–645 (2011). https://doi.org/10.1007/s11253-011-0530-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-011-0530-z