Skip to main content
SpringerLink
Log in

A block spin construction of ondelettes. Part I: Lemarié functions

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Using block spin assignments, we construct anL 2-orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions. These functions have exponential localization, and for even values of a construction parameterM one can make them classC M−1 with vanishing moments up to orderM inclusive. Such a basis has an important application to phase cell cluster expansions in quantum field theory.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lemarié, P., Meyer, Y.: Ondelettes et bases Hilbertiannes. Rev. Mat. Ibero-Am. (to appear)

  2. Meyer, Y.: Sémin. Bourbaki38, 662 (1985–86)

    Google Scholar 

  3. Lemarié, P.: Une nouvelle base d' ondelettes deL 2(ℝn). Ecole Normale Supérieure. Preprint

  4. Battle, G., Federbush, P.: A phase cell cluster expansion for euclidean field theories. Ann. Phys.142, (1), 95 (1982)

    Google Scholar 

  5. Battle, G., Federbush, P.: A phase cell cluster expansion for a hierarchical φ 43 model. Commun. Math. Phys.88, 263 (1983)

    Google Scholar 

  6. Battle, G., Federbush, P.: Ondelettes and phase cell cluster expansions, a vindication. Commun. Math. Phys. (in press)

  7. Williamson, C.: A phase cell cluster expansion of φ 43 . Ann. Phys. (to appear)

  8. Gawedzki, K., Kupiainen, A.: A rigorous block spin approach to massless lattice theories. Commun. Math. Phys.77, 31 (1980)

    Google Scholar 

  9. Federbush, P.: A phase cell approach to Yang-Mills theory. I. Modes, lattice-continuum duality. Commun. Math. Phys.107, 319–329 (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Cornell University, 14853, Ithaca, New York, USA

    Guy Battle

Authors
  1. Guy Battle
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

Supported in part by the National Science Foundation under Grant No. DMS 8603795 and by the Mathematical Sciences Institute

On leave from the Mathematics Department, Texas A & M University, College Station, Texas 77843 USA

Rights and permissions

Reprints and permissions

About this article

Cite this article

Battle, G. A block spin construction of ondelettes. Part I: Lemarié functions. Commun.Math. Phys. 110, 601–615 (1987). https://doi.org/10.1007/BF01205550

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01205550

Keywords

Search

Navigation