Representation of differential operators in wavelet basis

Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂x and ∂y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂x, ∂y) is derived, where g is an analytic function.