Approximation on the regular hexagon

Authors

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.

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

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

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

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

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

A. Guven, Approximation by Riesz means of hexagonal Fourier series, Z. Anal. Anwend. 36 (2017), 1-16, 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

A. Guven, Approximation of continuous functions on hexagonal domains, J. Numer. Anal. Approx. Theory. 47 (2018), 42-57.

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

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

L. Mcfadden, Absolute Norlund summability, Duke Math. J. 9 (1942), 168-207, 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.

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

F. Moricz, B. E. Rhoades, Approximation by N¨orlund 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

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

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

S. Prossdorf, Zur konvergenz der Fourierreihen h¨olderstetiger funktionen, Math. Nachr. 69 (1975), 7–14, 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).

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

L. Zhizhiashvili, Trigonometric Fourier series and their conjugates, Kluwer Academic Publishers (1996).

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

Downloads

Published

2021-02-22

How to Cite

Guven, A. (2021). Approximation on the regular hexagon. J. Numer. Anal. Approx. Theory, 49(2), 138-154. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1229

Issue

Section

Articles