Ondelettes and phase cell cluster expansions, a vindication

Abstract

Y. Meyer has recently developed a particularly useful o.n. basis for L 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.