Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-18T06:33:11.312Z Has data issue: false hasContentIssue false
  • English
  • Français

On Young's criteria for the convergence of Fourier series and their conjugates

Published online by Cambridge University Press:  24 October 2008

W. L. C. Sargent
W. L. C. Sargent
Affiliation:
Newnham College
Get access Rights & Permissions [Opens in a new window]

Extract

1. Young's criterion for the convergence of a Fourier series may be stated in the following form:

The integral

tends to zero as ω → ∞ whenever

(A) ø(t) is absolutely integrable in (0, a),

(B) ø(t) → 0 in mean as t → 0,

(C) tø(t) is of bounded variation to the immediate right of t = 0 and, as t → 0,

Type
Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 1 , January 1929 , pp. 26 - 30
Copyright
Copyright © Cambridge Philosophical Society 1929

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. and Littlewood, J. E., Math. Zeitschrift, vol. XIX (1923), 67–96.Google Scholar
2.Hardy, G. H. and Littlewood, J. E., Proc. London Math. Soc., (2) vol. XXVIII (1928), 301–311.CrossRefGoogle Scholar
3.S., Pollard, Journal London Math. Soc., vol. II (1927), 255–262.Google Scholar