Bohr’s theorem for double trigonometric interpolation polynomials
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2014), pp. 13-23
Cet article a éte moissonné depuis la source Math-Net.Ru
H. Bohr’s Theorem on uniform convergence of double trigonometric interpolation polynomials is proved.
Keywords:
trigonometric interpolation, homeomorphism
Mots-clés : superposition, convergence.
Mots-clés : superposition, convergence.
@article{UZERU_2014_2_a1,
author = {A. R. Nurbekyan},
title = {Bohr{\textquoteright}s theorem for double trigonometric interpolation polynomials},
journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
pages = {13--23},
year = {2014},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UZERU_2014_2_a1/}
}
TY - JOUR AU - A. R. Nurbekyan TI - Bohr’s theorem for double trigonometric interpolation polynomials JO - Proceedings of the Yerevan State University. Physical and mathematical sciences PY - 2014 SP - 13 EP - 23 IS - 2 UR - http://geodesic.mathdoc.fr/item/UZERU_2014_2_a1/ LA - en ID - UZERU_2014_2_a1 ER -
A. R. Nurbekyan. Bohr’s theorem for double trigonometric interpolation polynomials. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2014), pp. 13-23. http://geodesic.mathdoc.fr/item/UZERU_2014_2_a1/
[1] N.K. Bari, A Treatise on Trigonometric Series, Pergamon Press, 1964
[2] J.-P. Kahane, Y. Katznelson, Series de Fourier des Fonctions Bornees, Studies in Pure Mathematics, 1983, 395–410 | MR | Zbl
[3] A.A. Sahakian, “On Bohr’s Theorem for Multiple Fourier Series”, Mat. Zametki, 64:6 (1998), 913–924 | DOI | MR
[4] B.I. Golubov, “Double Fourier Series and Functions of Bounded Variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 12, 55–68 (in Russian) | MR | Zbl
[5] A. Zygmund, Trigonometric Series, ed. 2nd, Cambridge Univ. Press, New York, 1959 | MR | Zbl
[6] D. Waterman, H. Xing, “The Convergence of Partial Sums of Interpolating Polynomials”, J. Math. Anal. Appl., 333 (2007), 543–555 | DOI | MR | Zbl