Abstract
Exact values have been found, for the diameters in the sense of Kolmogorov of certain classes of functions with a Hardy metric, analytic in the unit circle, whose boundary values admit of a representation by a convolution or the averaged modulus of smoothness of their boundary values is majorized by a given function. In passing, certain extremal properties of trigonometric polynomials are established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. N. Kolmogorov, “über die best AnnÄherung von Funktionen einer gegebenen Funktion-klassen, ” Ann. Math.,37, 107–111 (1936).
K. I. Babenko, “On the best approximations of one class of functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,22, No. 5, 631–640 (1958).
V. M. Tikhomirov, “Diameters of sets in functional spaces and the theory of best approximations, ” Usp. Mat. Nauk,15, No. 3, 81–120 (1960).
L. V. Taikov, “On the best approximation in the mean of certain classes of analytic functions,” Mat. Zametki,1, No. 2, 155–162 (1967).
L. V. Taikov, “One circle of extremal problems for trigonometric polynomials,” Usp. Mat. Nauk,20, No. 3, 205–211 (1965).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 285–295, August, 1977.
Rights and permissions
About this article
Cite this article
Taikov, L.V. Diameters of certain classes of analytic functions. Mathematical Notes of the Academy of Sciences of the USSR 22, 650–656 (1977). https://doi.org/10.1007/BF01780976
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01780976