Skip to main content

Explicit Calculations and Asymptotic Behavior of a Distance Measure Between Finite Abelian Groups

Abstract

A metric on the space of finite abelian groups was introduced by Wolf. Though numerically computable for given groups, up to now hardly any theoretical results for this metric have been known. With a slight modification of the original definition, we are able to give a closed form for some distances and also gain some insight into the asymptotic behavior, i.e. the behavior as the group orders go to infinity.

This is a preview of subscription content, access via your institution.

References

  1. G. Larcher and G. Pirsic, Base change problems for generalized Walsh series and multivariate numerical integration, Pacific J. Math., 189 (1999), 75-105.

    Google Scholar 

  2. G. Larcher, W. Ch. Schmid, and R. Wolf, Representation of functions as Walsh series to different bases and an application to the numerical integration of high-dimensional Walsh series, Math. Comp., 63 (1994), 701-716.

    Google Scholar 

  3. G. Larcher, W. Ch. Schmid, and R. Wolf, Quasi-Monte Carlo methods for the numerical integration of multivariate Walsh series, Math. and Computer Modelling, 23 (1996), 55-67.

    Google Scholar 

  4. R. Wolf, A distance measure on finite abelian groups and an application to quasi-Monte Carlo integration, Acta Math. Hungar., 78 (1998), 25-37.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pirsic, G. Explicit Calculations and Asymptotic Behavior of a Distance Measure Between Finite Abelian Groups. Acta Mathematica Hungarica 91, 275–290 (2001). https://doi.org/10.1023/A:1010695216217

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010695216217

Keywords

  • Asymptotic Behavior
  • Theoretical Result
  • Abelian Group
  • Closed Form
  • Distance Measure