Representation in Lp by Series of Translates and Dilates of One Function Original Research Article

We study minimal conditions under which the function system of dyadic translates and dilates of one fixed function φt with support in [0, 1] forms a representation system in Lp(0, 1), i.e., that any function f(t) ∈ Lp(0, 1) can be represented by at least one Lp-convergent series with respect to this system. Generalizations to the situation of a multiresolution analysis on Rn are also discussed.