A study of orthonormal multi-wavelets on the interval
Siwang Zhou, Xieping Gao · International Journal of Computer Mathematics · 2006
The construction and properties of interval multi-wavelets based on orthonormal multi-wavelets on L 2(R) with arbitrary supports and multiplicity r are introduced. The interval multi-wavelets, which can preserve the polynomial reproduction order of corresponding multi-wavelets, are constructed and the decomposition and reconstruction formulas for interval multi-wavelet are obtained. We propose the “balancing” concept of the interval multi-wavelets and study the construction of orthogonal balancing multi-wavelets, which have been ignored in the past. We also study the symmetry of interval multi-wavelets and obtain necessary and sufficient conditions of it.