Pacific Journal of Mathematics

Trigonometric approximation theory in compact totally disconnected groups.

George Benke

Article information

Pacific J. Math., Volume 77, Number 1 (1978), 23-32.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
Secondary: 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol s kii-type inequalities) 41A25: Rate of convergence, degree of approximation 42A10: Trigonometric approximation 43A50: Convergence of Fourier series and of inverse transforms


Benke, George. Trigonometric approximation theory in compact totally disconnected groups. Pacific J. Math. 77 (1978), no. 1, 23--32.

Export citation


  • [1] S.Bernstein, Surordre dela meilleure approximation desfonctions continues pardes polynmes de degre donne, Mem. Acad. Roy. Belgique, 2me serie, 4 (1912), 1-104.
  • [2] W.Bloom, Jackson's theorem for locally compact ahelian groups, Bull. Aust. Math. Soc, 10 (1974), 59-66. 3# fJackson's theorem for finite products and homomorphic images of locally compact abelian groups, Bull. Aust. Math. Soc, 12 (1975), 301-309.
  • [4] W.Bloom, On the absolute convergence of trigonometric series (in Russian), Collected work, vol. 2,166-169.
  • [5] E. Hewitt andK. Ross, Abstract Harmonic Analysis II,Springer Verlag, Berlin, 1970.
  • [6] D. Jackson, Onapproximations bytrigonometrical sums and polynomials, Trans. Amer. Math. Soc, 13 (1912), 491-515.
  • [7] L.S.Pontryagin, Topological Groups, Gordon and Breach, Science Publishers, Inc., New York, 1966.
  • [8] P.Walker, Lipschitz classes onO-imensional groups, Proc Camb. Phil. Soc, 63 (1967), 923-928. 9# sLipschitz classes on finite dimensional groups, Proc. |Camb. Phil. Soc, 66 (1969), 31-38.
  • [10] A.Zygmund, Surlaconvergence absolue des series de Fourier, Proc London Math. Soc, 3 (1928), 194-196.