Abstract
In this paper we consider the uniform approximation of a function from a certain class by sums obtained as a result of some matrix transformation of the universal power lacunary series.
Similar content being viewed by others
References
D. E. Men’shov, “On Universal Trigonometric Series,” Sov. Phys. Dokl. 49(2), 79–82 (1945).
A. I. Seleznev, “On Universal Power Series,” Matem. Sborn. 28(2), 453–460 (1951).
C. K. Chui and M. N. Parnes, “Approximation by Overconvergence of a Power Series,” J. Math. Anal. Appl. 36(3), 693–696 (1971).
W. Luh, “Über den Satz von Mergelyan,” J. Approxim. Theory 16(2), 194–198 (1976).
A. F. Leont’ev, Sequences of Polynomials of Exponentials (Nauka, Moscow, 1980) [in Russian].
A. I. Seleznev, I. V. Motova, and V. A. Volokhin, “The Completeness of Systems of Functions and Universal Series,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 2, 84–90 (1977) [Soviet Mathematics (Iz. VUZ), 21 (11), 70–75 (1977)].
A. I. Seleznev and L. K. Dodunova, “On Two Theorems of Leont’ev on Completeness of Subsystems of Faber and Jacobi Polynomials,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 4, 51–55 (1982) [Soviet Mathematics (Iz. VUZ), 26 (4), 60–66 (1982)].
L. K. Dodunova, “A Generalization of the Universality Property of Faber Polynomial Series,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 12, 31–34 (1990) [Soviet Mathematics (Iz. VUZ), 34 (12), 37–40 (1990)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.V. Gosteva and L.K. Dodunova, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 3, pp. 3–8.
About this article
Cite this article
Gosteva, N.V., Dodunova, L.K. A generalization of the universality of power lacunary series. Russ Math. 56, 1–5 (2012). https://doi.org/10.3103/S1066369X12030012
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X12030012