A Tauberian Theorem for the Generalised Abel Method of Summability-I

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Authors

  • P. A. Jeyarajan
     Annamalai University, Annamalainagar ,IN

Abstract

This method was introduced independently by A. Amir Jakimovski ([2], p. 374) and C.T. Rajagopal ([8], p. 93). It was discussed in detail by D. Borwein [4]. In the sequence to function transformation method (Aα) if we put α = 0, we get the familiar Abel method (A0) or {A).

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Published

1972-12-01

How to Cite

Jeyarajan, P. A. (1972). A Tauberian Theorem for the Generalised Abel Method of Summability-I. The Journal of the Indian Mathematical Society, 36(3-4), 279–289. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/16670

Issue

Volume 36, Issue 3-4, September-December 1972

Section

Articles

License

Copyright (c) 1972 P. A. Jeyarajan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

A. AMIS JAKIMOVSKI: On a converse of Abel's Theorem, Proc. Amer. Math. Soc, Vol. 3 (1952), 244-56.

A. AMIR JAKIMOVSKI: Some relations between the methods of summability of Abel, Borel, Cesaro, Holder and Hausdorff, Journal a"Analyse Mathematique, Vol. 3 (1953-54), 346-81.

R. P. BOAS : Entire functions, New York, (1954).

D. BOBWEIN : On a scale of Abel-Type summability methods, Proc. Cambridge Phil. Soc, Vol. 53 (1957), 318-22.

L. S. BOSANQTJET: Note on convergence and summability factors (II), Proc. Lond. Math. Soc. (2), Vol. 50 (1949), 295-304.

G. H. HARDY : Divergent Series, Oxford, (1949).

W. B. JITRKAT : Ein funktionentheoretischer Beweis fur 0Taubersatze bei Potenzreihen, Archiv der Mathematik, Vol. 7 (1956), 122-25.

G. T. RAJAGOPAL: Theorems on the product of two summability methods with applications, Jour. Indian Math. Soc. Vol. 18 (1954), 89-105.

R. SCHMIDT : Ober divergente Folgen und lineare Mittelbildungen, Math. Zeit. Vol. 22 (1925), 89-152.

E. C. TITCHMARSH: The Theory of Functions, Oxford, (1952).