Using the Refinement Equation for Evaluating Integrals of Wavelets
Wolfgang Dahmen, Charles A. Micchelli · SIAM Journal on Numerical Analysis · 1993
The Wavelet Galerkin Method for solving partial differential equations leads to the problem of computing integrals of products of derivatives of wavelets. This paper studies the problem from the point of view of stationary subdivision schemes. One of the main results is to identify these integrals as components of the unique solution of a certain eigenvector-moment problem associated with the coefficients of the refinement equation. Asymptotic expansions for the corresponding subdivision schemes form an important ingredient of our approach.