This is a preview of subscription content, log in via an institution to check access.
Literature cited
G. Faber, “Über die interpolatorische Darstellung stetiger Functionen,” Jahrb. Dtsch. Math.,23, 192–210 (1914).
P. L. Ul'yanov, “On some solved and unsolved problems in the theory of orthogonal series,” Proceedings of the Fourth All-Union Mathematics Conference, Vol. 2, Izd. Akad. Nauk SSSR, Leningrad (1964), pp. 694–704.
G. Foias and I. Singer, “Some remarks on strongly linearly independent sequences and bases in Banach Spaces,” Rev. Roum. Math. Pures Appl.,6, No. 3, 589–594 (1961).
K. M. Shaidukov, “On the order of growth of the degrees of a polynomial basis,” Funkts. Anal. Teor. Funktsii (Kazan), No. 1, 134–138 (1963).
P. L. Ul'yanov, “Solved and unsolved problems in the theory of trigonometric and orthogonal series,” Usp. Mat. Nauk,19, No. 1, 3–69 (1964).
Z. A. Chanturiya, “On the bases of the space of continuous functions,” Mat. Sb.,88, No. 4, 589–608 (1972).
V. N. Temlyakov, “On the order of growth of the degrees of a polynomial basis in the space of continuous functions,” Mat. Zametki,22, No. 5, 711–727 (1977).
K. I. Babenko, “On bases in Hilbert space,” Dokl. Akad. Nauk SSSR,57, No. 5, 427–430 (1947).
S. V. Bochkarev, “Construction of an interpolation dyadic basis in the space of continuous functions on the basis of Fejér kernels,” Tr. Mat. Inst. Akad. Nauk SSSR,172, 29–59 (1985).
Z. A. Chanturiya, “On a generalization of G. Faber's theorem on polynomial bases,” Mat. Zametki,2, No. 2, 187–190 (1967).
S. A. Telyakovskii, “On the norms of linear polynomial operators,” Mat. Sb.,68, 561–569 (1965).
M. I. Kadets, “On relative projectional constants and on a theorem of Z. A. Chanturiya,” Soobshch. Akad. Nauk Gruz. SSR,74, No. 3, 541–543 (1974).
P. K. Suetin, Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1979).
A. Zygmund, Trigonometric Series, Vol. II, Cambridge University Press, London-New York (1959).
P. P. Korovkin, Linear Operators and Approximation Theory [in Russian], Fizmatgiz, Moscow (1959).
V. F. Nikolaev, “On operations relating polynomials to functions,” Dokl. Akad. Nauk SSSR,68, No. 1, 9–11 (1949).
N. A. Sapogov, “On the norms of linear polynomial operators in connection with the problems of approximation of continuous functions,” Vestn. Leningr. Univ. Mat., No. 13, 53–68 (1964).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 42, No. 2, pp. 207–214, August, 1987.
The author thanks S. B. Stechkin for his interest in this work.
Rights and permissions
About this article
Cite this article
Privalov, A.A. Growth of the degrees of polynomial bases and approximation of trigonometric projectors. Mathematical Notes of the Academy of Sciences of the USSR 42, 619–623 (1987). https://doi.org/10.1007/BF01240448
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01240448