Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.