Approximation on the regular hexagon

Authors

DOI:

https://doi.org/10.33993/jnaat492-1229
Abstract views: 247

Abstract

The degree of trigonometric approximation of continuous functions, which are periodic with respect to the hexagon lattice, is estimated in uniform and Hölder norms.

Approximating trigonometric polynomials are matrix means of hexagonal Fourier series.

Downloads

Download data is not yet available.

References

P. Chandra, On the generalized Fejer means in the metric of Holder space, Math. Nachr. 109 (1982), 39-45, https://doi.org/10.1002/mana.19821090105 DOI: https://doi.org/10.1002/mana.19821090105

P. Chandra, On the degree of approximation of a class of functions by means of Fourier series, Acta Math. Hung. 52 (1988), 199-205, https://doi.org/10.1007/bf01951564 DOI: https://doi.org/10.1007/BF01951564

B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal. 16 (1974), 101-121, https://doi.org/10.1016/0022-1236(74)90072-x DOI: https://doi.org/10.1016/0022-1236(74)90072-X

A. Guven, Approximation by means of hexagonal Fourier series in Holder norms, J. Classical Anal. 1 (2012), 43-52, https://doi.org/10.7153/jca-01-06 DOI: https://doi.org/10.7153/jca-01-06

A. Guven, Approximation by (C, 1) and Abel-Poisson means of Fourier series on hexagonal domains, Math. Inequal. Appl. 16 (2013), 175-191, https://doi.org/10.7153/mia-16-13 DOI: https://doi.org/10.7153/mia-16-13

A. Guven, Approximation by Riesz means of hexagonal Fourier series, Z. Anal. Anwend. 36 (2017), 1-16, https://doi.org/10.4171/zaa/1576 DOI: https://doi.org/10.4171/ZAA/1576

A. Guven, Approximation by Norlund means of hexagonal Fourier series, Anal. Theory Appl. 33 (2017), 384-400, https://doi.org/10.4208/ata.2017.v33.n4.8 DOI: https://doi.org/10.4208/ata.2017.v33.n4.8

A. Guven, Approximation of continuous functions on hexagonal domains, J. Numer. Anal. Approx. Theory. 47 (2018), 42-57, https://ictp.acad.ro/jnaat/journal/article/view/1128

A. S. B. Holland, B. N. Sahney and J. Tzimbalario, On degree of approximation of a class of functions by means of Fourier series, Acta Sci. Math. 38 (1976), 69-72

P. D. Kathal, A. S. B. Holland and B. N. Sahney, A class of continuous functions and their degree of approximation, Acta Math. Acad. Sci. Hungar. 30 (1977), 227-231, https://doi.org/10.1007/bf01896187 DOI: https://doi.org/10.1007/BF01896187

H. Li, J. Sun and Y. Xu, Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle, SIAM J. Numer. Anal. 46 (2008), 1653-1681, https://doi.org/10.1137/060671851 DOI: https://doi.org/10.1137/060671851

L. Mcfadden, Absolute Norlund summability, Duke Math. J. 9 (1942), 168-207, https://doi.org/10.1215/s0012-7094-42-00913-x DOI: https://doi.org/10.1215/S0012-7094-42-00913-X

R. N. Mohapatra and B. N. Sahney, Approximation of continuous functions by their Fourier series, Anal. Numer. Theor. Approx. 10 (1981), 81-87, https://ictp.acad.ro/jnaat/journal/article/view/1981-vol10-no1-art9

R. N. Mohapatra and P. Chandra, Degree of approximation of functions in the Holder metric, Acta Math. Hung. 41 (1983), 67-76, https://doi.org/10.1007/bf01994063 DOI: https://doi.org/10.1007/BF01994063

F. Moricz, B. E. Rhoades, Approximation by Norlund means of double Fourier series for Lipschitz functions, J. Approx. Theory 50 (1987), 341-358, https://doi.org/10.1016/0021-9045(87)90012-8 DOI: https://doi.org/10.1016/0021-9045(87)90012-8

F. Moricz, B. E. Rhoades, Approximation by Norlund means of double Fourier series to continuous functions in two variables, Constr. Approx. 3 (1987), 281-296, https://doi.org/10.1007/bf01890571 DOI: https://doi.org/10.1007/BF01890571

F. Moricz, X. L. Shi, Approximation to continuous functions by Cesaro means of double Fourier series and conjugate series, J. Approx. Theory 49 (1987), 346-377, https://doi.org/10.1016/0021-9045(87)90074-8 DOI: https://doi.org/10.1016/0021-9045(87)90074-8

S. Prossdorf, Zur konvergenz der Fourierreihen holderstetiger funktionen, Math. Nachr. 69 (1975), 7–14, https://doi.org/10.1002/mana.19750690102 DOI: https://doi.org/10.1002/mana.19750690102

B. N. Sahney and D. S. Goel, On the degree of approximation of continuous functions, Ranchii Univ. Math. J. 4 (1973), 50-53.

A. F. Timan, Theory of approximation of functions of a real variable, Pergamon Press (1963). DOI: https://doi.org/10.1016/B978-0-08-009929-3.50008-7

Y. Xu, Fourier series and approximation on hexagonal and triangular domains, Constr. Approx. 31 (2010), 115-138, https://doi.org/10.1007/s00365-008-9034-y DOI: https://doi.org/10.1007/s00365-008-9034-y

L. Zhizhiashvili, Trigonometric Fourier series and their conjugates, Kluwer Academic Publishers (1996). DOI: https://doi.org/10.1007/978-94-009-0283-1

A. Zygmund, Trigonometric series, Vols. I-II, Cambridge Univ. Press, 2nd edition (1959)

Downloads

Published

2020-12-31

How to Cite

Guven, A. (2020). Approximation on the regular hexagon. J. Numer. Anal. Approx. Theory, 49(2), 138–154. https://doi.org/10.33993/jnaat492-1229

Issue

Section

Articles