Approximation of continuous functions by typical means of their Fourier series

@inproceedings{Aljani1961ApproximationOC,
  title={Approximation of continuous functions by typical means of their Fourier series},
  author={S. Aljan{\vc}i{\'c}},
  year={1961}
}
1. Notations and results, (i) Let C be the class of continuous and periodic functions/of period 27r such that fl*f(x)dx = 0. The Lipschitz and Zygmund class M'A«, and M2Aa or simply 'A,* and 2A« (0<agl) are defined by \f(x+h) -fix) | gM| h\a and \f(x+h)+f(x-h) -2f(x)\ ^M\h\" respectively. Though 1Aa = 2Aa if 0<a<l, it is sometimes convenient to preserve for 0<«<1 both notations, even the neutral one Aa. By MWT(ß) or simply by Wr(ß), r>0, ß real, we denote the class of functions /G C whose… Expand
7 Citations

References

SHOWING 1-9 OF 9 REFERENCES
a) Classe de saturation des procédés de sommation de Holder et de Riesz, C
  • R. Acad. Sei. Paris vol. 246 (
  • 1958
Sur l'ordre de grandeur de l'approximation d'une fonction par les moyennes de sa série de Fourier
  • Mat. Fiz. Lapok vol
  • 1941
On determination of the class of saturation in the theory of approximation of functions
  • 28
Steckin , On the best approximation of some classes of periodic functions by trigonometric polynomials ( in Russian ) , Izv . Akad . Nauk SSSR
  • 1956
Steckin, On the best approximation of some classes of periodic functions by trigonometric polynomials (in Russian)
  • Izv. Akad. Nauk SSSR. Ser. Mat. vol
  • 1956
Sur une classe générale de procédés de sommation pour les séries de Fourier
  • Hungarica Acta Math. vol. 1, no
  • 1948
Approximation of periodic functions by trigonometrical polynomials (in Russian)
  • Trudy Mat. Inst. Steklov vol
  • 1945
The approximation of functions by typical means of their Fourier series
  • 70
On the Analytical Theory of Semi-Groups.
  • E. Hille
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1942
  • 21
  • PDF