Approximate Wavelets and the Approximation of Pseudodifferential Operators
Copyright policy )Approximate Wavelets and the Approximation of Pseudodifferential Operators
The paper studies an approximate multiresolution analysis for spaces generated by smooth functions which provide high order cubature formulas for integral operators of mathematical physics. Since these functions satisfy refinement equations with any prescribed accuracy methods of the wavelet theory can be applied. We obtain a decomposition of the finest scale space into almost orthogonal wavelet spaces. For one example we study some properties of the analytic prewavelets, describe the projection operators onto the wavelet spaces and consider some applications to the cubature of integral operators.
- Linköping University Sweden
- Weierstrass Institute Germany
- Leibniz Association Germany
- Weierstrass Institute for Applied Analysis and Stochastics Germany
ddc:510, Integral operators, approximate multiresolution analysis, sparse and semi-analytic representations of integral operators, almost orthogonal wavelet spaces, Applied Mathematics, article, Pseudodifferential operators as generalizations of partial differential operators, Nontrigonometric harmonic analysis involving wavelets and other special systems, Numerical methods for integral equations, Cubature formulas -- approximate multiresolution -- multivariate wavelets, approximate multiresolution, 510, approximate wavelets, Cubature formulas, multivariate wavelets, Numerical methods for wavelets, 65D30, Spectral, collocation and related methods for boundary value problems involving PDEs, 41A30, 41A63, pseudodifferential operators
ddc:510, Integral operators, approximate multiresolution analysis, sparse and semi-analytic representations of integral operators, almost orthogonal wavelet spaces, Applied Mathematics, article, Pseudodifferential operators as generalizations of partial differential operators, Nontrigonometric harmonic analysis involving wavelets and other special systems, Numerical methods for integral equations, Cubature formulas -- approximate multiresolution -- multivariate wavelets, approximate multiresolution, 510, approximate wavelets, Cubature formulas, multivariate wavelets, Numerical methods for wavelets, 65D30, Spectral, collocation and related methods for boundary value problems involving PDEs, 41A30, 41A63, pseudodifferential operators
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