Fractals Range functions Shift-invariant space Wavelets Frames LCA groups Fixed points Functional equation Sampling Self-similarity Shift-invariant spaces Dilation equation Fibers Refinement equation Riesz basis Theorem proving Affine systems Cantor set Harmonic analysis Image reconstruction Mathematical operators Multiwavelets Shift invariant spaces Translation invariant space Accuracy; approximation by translates; dilation equations; dilation matrix; multidimensional refinable functions; multidimensional wavelets; multiwavelets; refinement equations; refinable functions; shift invariant spaces; wavelets Algorithms Anisotropic function spaces Approximation theory Besov spaces Block codes