Abstract
For entire transcendental functions of finite generalized order, we obtain limit relations between the growth characteristic indicated above and sequences of their best polynomial approximations in certain Banach spaces (Hardy spaces, Bergman spaces, and spaces \(B\left( {p,q,{\lambda }} \right)\)).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
I. K. Daugavet, Introduction to the Theory of Approximation of Functions [in Russian], Leningrad University, Leningrad (1977).
R. S. Varga, “On an extension of a result of S. N. Bernstein,” J. Approxim. Theory, 1, No. 2, 176–179 (1968).
A. R. Reddy, “Approximation of an entire function,” J. Approxim. Theory, 3, No. 1, 128–137 (1970).
A. R. Reddy, “Best polynomial approximation to certain entire functions,” J. Approxim. Theory, 5, No. 1, 97–112 (1972).
M. N. Sheremeta, “On relationship between the growth of the modulus of an entire function and the moduli of the coefficients of its power expansion,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 100–108 (1967).
M. N. Sheremeta, “On relationship between the growth of entire functions or zero-order functions analytic in a circle and the coefficients of their power expansion,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 6, 115–121 (1968).
S. K. Balashov, “On relationship between the growth of an entire function of generalized order, the coefficients of its power expansion, and the distribution of roots,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 8, 10–18 (1972).
S. M. Shan, “Polynomial approximation of an entire function and generalized orders,” J. Approxim. Theory, 19, No. 4, 315–324 (1977).
A. V. Batyrev, “On the best polynomial approximation of analytic functions,” Dokl. Akad. Nauk SSSR, 76, No. 2, 173–175 (1951).
I. I. Ibragimov and N. I. Shikhaliev, “On the best polynomial approximation of analytic functions in a space of analytic functions,” Dokl. Akad. Nauk SSSR, 227, No. 2, 280–283 (1976).
A. Giroux, “Approximation of entire functions over bounded domains,” J. Approxim. Theory, 28, No. 1, 45–53 (1980).
S. B. Vakarchuk, “On the best polynomial approximation of entire transcendental functions in Banach spaces. I,” Ukr. Mat. Zh., 47, No. 9, 1123–1133 (1994).
S. B. Vakarchuk, “On the best polynomial approximation of entire transcendental functions in Banach spaces. II,” Ukr. Mat. Zh., 47, No. 10, 1318–1322 (1994).
S. B. Vakarchuk, “On the best polynomial approximation of functions analytic in the unit circle in Banach spaces,” Mat. Zametki, 55, No. 4, 6–14 (1994).
M. I. Gvaradze, “On one class of spaces of analytic functions,” Mat. Zametki, 21, No. 2, 141–150 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vakarchuk, S.B., Zhir, S.I. On Some Problems of Polynomial Approximation of Entire Transcendental Functions. Ukrainian Mathematical Journal 54, 1393–1401 (2002). https://doi.org/10.1023/A:1023407416027
Issue Date:
DOI: https://doi.org/10.1023/A:1023407416027