Abstract

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.

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