Skip to main content
Log in

Tauberian theorems for Borel-type methods of summability

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. N. H. Bingham, Tauberian theorems for summability methods of random-walk type. J. London Math. Soc. (2)30, 281–284 (1984).

    Google Scholar 

  2. D. Borwein, On methods of summability based on power series. Proc. Roy. Soc. Edinburgh Sect. A64, 342–349 (1957).

    Google Scholar 

  3. D. Borwein, A Tauberian theorem for Borel-type methods of summability. Canad. J. Math.21, 740–747 (1969).

    Google Scholar 

  4. D. Borwein andW. Kratz, On relations between weighted means and power series methods of summability. J Math. Anal. Appl.139, 178–186 (1989).

    Google Scholar 

  5. D. Borwein andT. Markovich, A Tauberian theorem concerning Borel-type and Cesàro methods of summability. Canad. J. Math.40, 228–247 (1988).

    Google Scholar 

  6. D. Borwein andI. J. W. Robinson, A Tauberian theorem for Borel-type methods of summability. J. Reine Angew. Math.273, 153–164 (1975).

    Google Scholar 

  7. G. H. Hardy, Properties of logarithmico-exponential functions. Proc. London Math. Soc. (2)10, 54–90 (1911).

    Google Scholar 

  8. G. H.Hardy, Divergent series. Oxford 1949.

  9. G. H. Hardy andJ. E. Littlewood, Theorems concerning the summability of series by Borel's exponential method. Rend. Circ. Mat. Palermo41, 36–53 (1916).

    Google Scholar 

  10. W. B. Jurkat, Ein funktionentheoretischer Beweis fürO-Taubersätze bei den Verfahren von Borel und Euler-Knopp. Arch. Math.7, 278–283 (1956).

    Google Scholar 

  11. W. Kratz andU. Stadtmüller, Tauberian theorems forJ p-summability. J. Math. Anal. Appl.139, 362–371 (1989).

    Google Scholar 

  12. W. Kratz andU. Stadtmüller, Tauberian theorems for generalJ p -methods and a characterization of dominated variation. J. London Math. Soc. (2)39, 145–159 (1989).

    Google Scholar 

  13. W.Kratz and U.Stadtmüller,O-Tauberian theorems forJ p -methods with rapidly increasing weights. J. London Math. Soc. (2), to appear 1990.

  14. F. W. J.Olver, Introduction to Asymptotics and Special Functions. New York-London 1974.

  15. R. Schmidt, Die Umkehrsätze des Borel'schen Summierungsverfahrens. Schriften Königsberg1, 205–256 (1925).

    Google Scholar 

  16. E. C.Titchmarsh, The theory of functions. Oxford 1939.

  17. G. Valiron, Remarques sur la sommation des séries divergentes par les méthodes de M. Borel. Rend Circ. Mat. Palermo42, 267–284 (1917).

    Google Scholar 

  18. T. Vijayaraghavan, A theorem concerning the summability of series by Borel's method. Proc. London Math. Soc. (2)27, 316–326 (1928).

    Google Scholar 

  19. K.Zeller und W.Beekmann, Theorie der Limitierungsverfahren. Berlin-Heidelberg-New York 1970.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kratz, W., Stadtmüller, U. Tauberian theorems for Borel-type methods of summability. Arch. Math 55, 465–474 (1990). https://doi.org/10.1007/BF01190268

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01190268

Keywords

Navigation