This group of papers deals with the analytical uses of continuous wavelet transforms. As it turns out, Hermitian wavelets (the `Mexican hat' family) are fundamentally related to the diffusion operator.

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Equations are a language.

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v Wavelet dynamics of the laminar-turbulent interface,

The Turbulent Years: John Lumley at 70, Symposium at Cornell Univ., June 2001 --- To be submitted, Phys. Fluids (2001).

v On a class of solutions for the inverse diffusion problem,

Appl. Math. Lett. 14, 617-624 (2001). Non-differential expressions for the Navier-Stokes nonlinear terms, and the emergence of turbulent structures, to be submitted (2001).

v A filtering and wavelet formulation for incompressible turbulence,

J. Turbulence 1,004, 1-16 (2000).

v Formal improvements in the solution of the wavelet-transformed Poisson and diffusion equations,

J. Math. Phys. 39, 4119-4128 (1998).

v A Hamiltonian Formulation for the Diffusion Equation,

Physical Review E 55, 1590-1599 (1997).

v Wavelet Transforms of some Equations of Fluid Mechanics,

Acta Mechanica 104, 1-25 (1994).

v Wavelet Transforms of the Navier-Stokes Equations and the Generalized Dimensions of Turbulence,

Appl. Sci. Res. 51, 109-113 (1993).

v Energy Dissipation in the Wavelet-Transformed Navier-Stokes Equations,

Phys. Fluids A5, 1512-1513 (1993).

v On the effect of boundary conditions on the multifractal statistics of incompressible turbulence,

IMA Conference on Multiscale Stochastic Processes Analyzed using multifractals and wavelets (1993).