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