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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.