Formal improvements in the solution of the wavelet-transformed poisson and diffusion equations

Hermitian wavelets' relation to the Laplace operator leads to a natural measure of the scale factor that emphasizes the largest component wave number. For the Poisson equation (e.g. the pressure equation in Navier-Stokes turbulence), the wavelet transform of the solution at a given location and scale depends on the wavelet transform of the source field at the same location and at nearby and larger scales. For the diffusion problem, the Hamiltonian formulation is simplified through a canonical transformation.