Skip to main content
Log in

Ondelettes and phase cell cluster expansions, a vindication

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

Abstract

Y. Meyer has recently developed a particularly useful o.n. basis forL 2(R d). Expansions using this basis, i.e. expansions into “ondelettes” or “wavelets,” have yielded important new results in soft and hard analysis. The expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions, a formalism already developed by the authors using other related bases. Adoption of ondelettes expansions into the phase cell program gives improvements of some extant results, and excises an early error.

Ondelettes lend more elegance to the phase cell cluster expansion of φ 43 , and to us are a vindication of the fundamental nature of this approach. This provides more promise for future developments.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Battle, G., Federbush, P.: Ann. Phys.142, 95–139 (1982)

    Google Scholar 

  2. Battle, G., Federbush, P.: Commun. Math. Phys.88, 263–293 (1983)

    Google Scholar 

  3. Daubechies, I.: Private communication

  4. Federbush, P.: Commun. Math. Phys.81, 327–340 and 341–360 (1981)

    Google Scholar 

  5. Meyer, Y.: La transformation en ondelettes (to be published)

  6. Williamson, C.: A phase cell cluster expansion for φ 43 , Missouri. Preprint

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Jaffe

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

This work was supported in part by the National Science Foundation under Grants No. PHY 85-02074 and

Rights and permissions

Reprints and permissions

About this article

Cite this article

Battle, G., Federbush, P. Ondelettes and phase cell cluster expansions, a vindication. Commun.Math. Phys. 109, 417–419 (1987). https://doi.org/10.1007/BF01206144

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01206144

Keywords

Navigation