Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T01:41:51.013Z Has data issue: false hasContentIssue false
  • English
  • Français

On Methods of Summability Based on Integral Functions. II

Published online by Cambridge University Press:  24 October 2008

D. Borwein
D. Borwein
Affiliation:
St Salvator's CollegeSt Andrews
Get access Rights & Permissions [Opens in a new window]

Extract

In two recent papers ((l), (2)) I investigated inclusion relations between IF (integral function) methods of summability. In the present paper the investigation is continued with the aid of standard Mellin transform theory and results due to Rogosinski and to Kuttner.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 2 , April 1960 , pp. 125 - 131
Copyright
Copyright © Cambridge Philosophical Society 1960

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)Borwein, D., On methods of summability based on power series. Proc. Roy. Soc. Edinb. 64 (1957), 343–9.Google Scholar
(2)Borwein, D., On methods of summability based on integral functions. Proc. Camb. Phil. Soc. 55 (1959), 23–30.CrossRefGoogle Scholar
(3)Hardy, G. H., Orders of infinity (Cambridge, 1910).Google Scholar
(4)Hardy, G. H., Divergent series (Oxford, 1949).Google Scholar
(5)Knopp, K., Bemerkung zum Borelschen limitierungsverfahren. R.C. Circ. mat. Palermo, 54 (1930), 331–4.Google Scholar
(6)Kuttner, B., A generalization of Abel summability. Proc. Camb. Phil. Soc. 32 (1936), 541–59.CrossRefGoogle Scholar
(7)Rogosinski, W. W., On Hausdorff methods of summability. Proc. Camb. Phil. Soc. 38 (1942), 166–92.CrossRefGoogle Scholar
(8)Titchmarsh, E. C., Theory of Fourier integrals (Oxford, 1937)Google Scholar