Approximate wavelets and the approximation of pseudodifferential operators
In this interesting paper, the authors introduce an approximate multiresolution analysis for spaces generated by smooth functions providing high-order semi-analytic cubature formulas for multidimensional integral operators of mathematical physics. Since these functions satisfy refinement equations with any prescribed accuracy, wavelet-type methods can be applied. An approximate decomposition of the finest scale space into almost orthogonal wavelet spaces is obtained. For the Gaussian function, properties of analytic prewavelets are studied and the projections onto the wavelet spaces are described. The wavelets retain the property of the scaling function to provide efficient analytic expressions of important integral operators, which leads to sparse and semi-analytic representations of these operators.
sparse and semi-analytic representations of integral operators
scientific article; zbMATH DE number 1310893
scientific article