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

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.Supported in part by the National Science Foundation under Grant No. DMS 8603795 and by the Mathematical Sciences InstituteOn leave from the Mathematics Department, Texas A & M University, College Station, Texas 77843 USA