Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T08:56:36.918Z Has data issue: false hasContentIssue false
  • English
  • Français

On the convergence factor of a Fourier series

Published online by Cambridge University Press:  24 October 2008

R. Mohanty
R. Mohanty
Affiliation:
Ravenshaw College, Cuttack, India
Get access Rights & Permissions [Opens in a new window]

Extract

Definition A. Let 0 < λ0 < λ1 < λ2 < …, λn → ∞ and suppose thatis a given infinite series write

where λm ≤ ω > λm+1. Also write for k > 0,

.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 129 - 132
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hardy, G. H.On the summability of Fourier series. Proc. London. Math. Soc. (2), 12 (1913), 365–72.CrossRefGoogle Scholar
(2)Hardy, G. H.The summability of a Fourier series by logarithmic means. Quart. J. Math. Oxford series 11 (1931), 107–12.Google Scholar
(3)Hardy, G. H.Divergent series, page 87 (Oxford 1963).Google Scholar
(4)Hardy, G. H. and Riesz, M.The general theory of Dirichlet's series (Cambridge, 1915).Google Scholar
(5)Misra, M. L.On the determination of the jump of a function by its Fourier coefficients. Quart. J. Math. Oxford series 18 (1947), 147–56.Google Scholar