15 research outputs found
Representation of differential operators in wavelet basis
AbstractExisting 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 âx and ây are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(âx, ây) is derived, where g is an analytic function