This is a preview of subscription content, log in via an institution to check access.
References
N. Wiener, “The quadratic variation of a function and its Fourier coefficients,” Mass. J. Math.,3, 72–94 (1924).
A. P. Terekhin, “Approximation of functions of bounded p-variation,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 171–187 (1965).
B. S. Kashin and A. A. Saakyan, Orthogonal Series [in Russian], Nauka, Moscow (1984).
E. R. Love and L. C. Young, “On fractional integration by parts,” Proc. London Math. Soc. (2),44, 1–35 (1938).
A. P. Terekhin, “Functions of bounded p-variation with a given order of the modulus of p-continuity,” Mat. Zametki,12, No. 5, 523–530 (1972).
B. I. Golubov, A. V. Efimov, and V. A. Skvortsov, Walsh Series and Transformations [in Russian], Nauka, Moscow (1987).
P. L. Ul'yanov, “Series with respect to the Haar system,” Mat. Sb.,63, No. 3, 356–391 (1964).
P. L. Ul'yanov, “An absolute and uniform convergence of the Fourier series,” Mat. Sb.,72, No. 2, 193–225 (1967).
B.I. Golubov, “Fourier series of continuous functions with respect to the Haar system, “ Izv. Akad. Nauk SSSR, Ser. Mat.,28, No. 6, 1271–1296 (1964).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 53, No. 6, pp. 11–21, June, 1993.
The author expresses his gratitude to Professor B. I. Golubov for stating the problem and for his valuable advice.
Rights and permissions
About this article
Cite this article
Volosivets, S.S. Approximation of functions of bounded p-variation by means of polynomials of the Haar and Walsh systems. Math Notes 53, 569–575 (1993). https://doi.org/10.1007/BF01212591
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01212591