Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-23T09:29:37.720Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute Riesz summability factors for Fourier series

Published online by Cambridge University Press:  20 January 2009

Prem Chandra
Prem Chandra
Affiliation:
Department of Mathematics, GOvernment Science College, Jabalpur (India)
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let ∑an be a given infinite series and {λn} a non-negative, strictly increasing, monotonic sequence, tending to infinity with n. We write, for w > λ0,

and, for r>0, we write

is known as the Riesz sum of “ type ” λn and “ order ” r, and

is called the Riesz mean of type λn and order r.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 65 - 70
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Mohanty, R., A criterion for the absolute convergence of a Fourier series, Proc. London Math. Soc. (2) 51 (1950), 186–196.Google Scholar
(2) Mohanty, R., On the absolute Riesz summability of Fourier series and allied series, Proc. London Math. Soc. (2) 52 (1951), 259–320.Google Scholar
(3) Obrechkoff, N., Sur la sommation absolue des séries de Dirichlet, C. R. Acad. Sci. Paris 186 (1928), 215–217.Google Scholar
(4) Obrechkoff, N., Über die absolute Summierung der Dirichletschen Reihen, Math. Zeitschrift 30 (1929), 375–386.CrossRefGoogle Scholar
(5) Riesz, M., Sur les séries de Dirichlet et les séries entières, C. R. Acad. Sci. Paris 149 (1909), 909–912.Google Scholar