Skip to main content Accessibility help
×
Home

Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers

  • Christian Berg (a1) and Antonio J. Durán (a2)

Abstract

We introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: $T\left( {{\left( {{a}_{n}} \right)}_{n}} \right)\,=\,1/\left( {{a}_{0}}\,+\cdots +\,{{a}_{n}} \right).$ We give some examples of Hausdorff moment sequences arising from the transformations and provide the corresponding measures: one of these sequences is the reciprocal of the harmonic numbers ${{\left( 1+1/2\,+\cdots +\,1/\left( n+1 \right) \right)}^{-1}}.$

    • 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.

      Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers
      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.

      Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers
      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.

      Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers
      Available formats
      ×

Copyright

References

Hide All
[B] Berg, C., Quelques remarques sur le cône de Stieltjes. In: Seminar on Potential Theory, Lecture Notes in Math. 814, Springer-Verlag, Berlin, 1980.
[BCR] Berg, C., Christensen, J. P. R., and Ressel, P., Harmonic analysis on semigroups. In: Theory of Positive Definite and Related Functions, Graduate Texts in Mathematics 100, Springer-Verlag, New York, 1984.
[BD] Berg, C. and Durán, A. J., A transformation from Hausdorff to Stieltjes moment sequences. Ark. Mat. 42(2004), 239257.
[BF] Berg, C. and Forst, G., Potential theory on locally compact abelian groups. Ergebnisse der Mathematik und ihrer Grenzgebiete 87. Springer-Verlag, New York, 1975.
[Bt] Bertoin, J., Lévy Processes. Cambridge Tracts in Mathematics 121, Cambridge University Press, Cambridge, 1996.
[D] Donoghue, W. F., Jr., MonotoneMatrix Functions and Analytic Continuation. Die Grundlehren der mathematischenWissenschaften 207, Springer-Verlag, New York, 1974.
[GR] Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series And Products. Academic Press, New York, 1980.
[GKP] Graham, R. L., Knuth, D. E., and Patashnik, O., Concrete Mathematics: A Foundation For Computer Science. Second ed. Addison, Wesley, Reading, MA: 1994.
[H] Hausdorff, F.,Momentprobleme für ein endliches Intervall. Math. Z. 16(1923) 220248.
[I] It ô, M., Sur les cônes convexes de Riesz et les noyaux complètement sous-harmoniques. Nagoya Math. J. 55(1974), 111144.
[R] Reuter, G. E. H., Über eine Volterrasche Integralgleichung mit totalmonotonem Kern. Arch. Math. 7(1956), 5966.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Related content

Powered by UNSILO

Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers

  • Christian Berg (a1) and Antonio J. Durán (a2)

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.