WAVELETS AND EXPECTATIONS: A DIFFERENT PATH TO WAVELETS

Independent of the other communities who have developed theories of wavelets over the last twenty years, we developed over the same period a view of wavelets seen as stochastic processes. That context arose naturally from our theory of Time operators in statistical mechanics. Essential ingredients in our theory included Kolmogorov dynamical systems and conditional expectations. The purpose of the present paper is to come up-to-date on the relationship of our theory to the general theory of wavelets.