Ondelettes and phase cell cluster expansions, a vindication

Y. Meyer has recently developed a particularly useful o.n. basis for L2(Rd). 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 ondelette expansions into the phase cell program gives improvements of some extant results, and excises and early error. Ondelettes lend more elegance to the phase cell cluster expansion of φ34, and to us are a vindication of the fundamental nature of this approach. This provides more promise for future developments. (orig.)