Skip to main content Accessibility help
×
Home

Absolute Tauberian Constants for Hausdorff Transformations

  • Soraya Sherif (a1)

Extract

Let be a fixed sequence of real or complex numbers. The Hausdorff transform {tn } of a sequence \sn) by means of the fixed sequence (or, in short, the (H, μn ) transform) is given by

where, for r, q ≧ 0,

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Absolute Tauberian Constants for Hausdorff Transformations
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Absolute Tauberian Constants for Hausdorff Transformations
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Absolute Tauberian Constants for Hausdorff Transformations
      Available formats
      ×

Copyright

References

Hide All
1. Bateman, H., Higher transcendental functions, Volume 1 (McGraw-Hill, New York, 1953).
2. Fekete, M., Vizsálatok az absolut summabilis sorokrol, alkalmazással a Direchlet éss Fourier —sorokra, math, és Termés. Ért. 32 (1914), 389425.
3. Hardy, G. H., Divergent series (Oxford Univ. Press, Oxford, 1940).
4. Hyslop, J. M., A Tauberian theorem for absolute summability, J. London Math. Soc. 12 (1937), 176180.
5. Jakimovski, A., The sequence-to-function analogues to Hausdorff transformations, The Bull, of the Research Council of Israel. Vol. 8F, No. 3 (1960), 135154.
6. Knopp, K. and Lorentz, G. G., Belträge Zür absoluten Limitierung. Arch. Math. (Basel) 2 (1949), 1016.
7. Maddox, I. J., Elements of functional analysis (Cambridge Univ. Press, 1970).
8. Mears, F. M., Absolute regularity and the Norlund mean, Ann. of Math. 83 (1937), 594601.
9. Sherif, S., Absolute Tauberian constants for Cesaro means, Trans. Amer. Math. Soc. 168 (1972), 233-241.
10. Whittaker, J.M., The absolute summability of Fourier series, Proc. Edinburgh Math. Soc. 2 (1931), 15.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Absolute Tauberian Constants for Hausdorff Transformations

  • Soraya Sherif (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed